Journal articles on the topic 'Consecutive k-out-of-m-from-n'

  Abstract: The consecutive-k-out-of-m-from-n: F system with multiple failure criteria consists of n sequentially ordered components (,). The system fails if among any  consecutive components there are at least  components in the failed state. In this paper, the ordinary consecutive-k-out-of-m-from-n: F system played a pivotal role in achieving the reliability and failure probability functions of the consecutive-k-out-of-m-from-n: F linear and circular system with multiple failure criteria. We proved that the failure states of the multiple failure criteria system is a union of all failure state of the consecutive--out-of--from-n: F system, while the functioning state is an intersection of  the functioning states of the consecutive--out-of--from-n: F system for . The maximum number of failed components of the functioning consecutive k-out-of-m-from-n: F system with multiple failure criteria is computed.   اقتران موثوقية و اقتران احتمال فشل النظام التتابعي k-out-of-m-from-n: F متعدد معايير الفشل   ملخص: يتكون النظام  التتابعي k-out-of-m-from-n: F  متعدد معايير الفشل من n من المكونات أو الأجزاء، والذي يفشل إذا حدث انه خلال أي من  المكونات المتتابعة يفشل خلالها  على الأقل عدد من المكونات. في هذا البحث تم استنتاج اقتران الكثافة الاحتمالي للموثوقية والفشل لهذا النظام من خلال استخدام طبيعة ومكونات النظام العادي ذو الشرط الوحيد k-out-of-m-from-n: F، فلقد أثبتنا أن حالات الفشل للنظام التتابعي متعدد معايير الفشل هو فعليا اتحاد لحالات الفشل للنظام التتابعي ذو الشرط الوحيد(-out-of--from-n: F) ، أما حالات العمل للنظام التتابعي متعدد معايير الفشل  فهي تقاطع حالات العمل للنظام التتابعي ذو الشرط الوحيد  (-out-of--from-n: F) ، خلال هذا كله، تم حساب العدد الأقصى للمكونات أو الأجزاء التي ممكن أن تفشل بحيث يبقى النظام ككل في حالة العمل. الكلمات المفتاحية: النظام التتبعي ذو الشرط الوحيد، اقتران موثوقية ، احتمال فشل النظام التتبعي.  

A 3-dimensional consecutive k-out-of-n : F system consists of n3 components disposed on a cubic grid of size n; it fails if and only if all the components of at least one cube of size k (1 < k < n) fail (k3 components). Although introduced as early as in 1992 by Salvia and Lasher7 as a better model for problems in medical imaging, few results are known about it.1 In this paper, we propose, in the the independent and not-necessarily-identical case, a new lower bound which has the advantage of being calculated directly from the reliability of a one dimensional consecutive-k-out-of-n:F system. To do this, we derive an intermediate system2 which behaves like a one dimensional consecutive k-out-of-n and is less reliable than the initial 3-dimensional system, hence its suitability as the lower bound. The proposed approach converts a three-dimensional system into a one-dimensional system directly. It can be extended to the three-dimensional versions of the k-within-connected-(r,s,t)-out-of-(m,n,p):F system and the m-consecutive-k-out-of-n : F system.

A "consecutive-k-out-of-m-from-n:F system" consists of n linearly or cyclically ordered components. The system fails if and only if there exist m consecutive components among them at least k ones are failed. In this paper we consider such a system with identical components and we give under some conditions a good approximation for the unreliability of the system when the number of components becomes large. More precisely, the purpose of the present paper is to show that for any failure distribution of components the limit law of the system's unreliability is always of the Weibull class. Thus we generalize here the result given in the case when the failure distribution of components is of the Weibull. We give also some numerical examples.

ABSTRACT BACKGROUND: Klebsiella pneumoniae on these days show greater resistance towards newer generation cephalosporin. The present study made an effort to show the relevance between ESBL producing K. pneumoniae and virulence determinant in respect to serum resistance and K1, K2 antigens at a tertiary care hospital in South India. MATERIAL AND METHODS: A total of 520 consecutive, non-duplicate isolates of K. pneumoniae were recovered from various clinical specimens such as Urine (n = 360), sputum (n = 107), pus (n = 25), blood (n = 6) and other miscellaneous specimens (n=22) obtained from both out patients and in patients between June 2012 to July 2016 were included in the study. RESULTS: Polymerase Chain Reaction to detect bla genes in 62 isolates phenotypically identified as ESBL producers were successful in 58 (93.54%) isolates. Of the 13 ESBL producing hypermucoviscous Klebsiella pneumoniae (hvKP) strains, 6 of them were showing the amplicons for gene's coding for K1 antigens. CONCLUSION: The study provides further authentication of the global sporadic of bla CTX-M and the relevance between K antigens and serum resistance with ESBL production in our place. As there is no much study available, it also highlights the need for further study of their epidemiological surveillance.

Purpose The purpose of this paper is to deal with a linear multi-state sliding window coherent system which generalizes the consecutive k-out-of-r-from-n:F system in the multi-state case. The system has n linearly ordered multi-state elements consisting of m parallel independent and identically distributed elements. Every element of the system can have two states: completely working or totally failed. The system fails if the sum of performance rate is lower than the given weight. Design/methodology/approach The authors proposed to compute the signature, MTTF and Barlow–Proschan index with the help of UGF technique of multi-state SWS which consists of m parallel i.i.d. components in each multi-state window. Findings In the present study, the authors have evaluated the signature reliability, expected lifetime, cost analysis and Barlow–Proschan index. Originality/value In this study, the authors have studied a linear multi-state sliding window system which consists of n ordered multi-state element, and each multi-state element also consists of m parallel windows. The focus of the present paper is to evaluate reliability metrices of the considered system with the help of signature from using the universal generating function.

A field experiment on fruit based agroforestry systems comprising of one silvi (<em>Alnus nepalensis</em>), two fruit trees, (<em>Citrus reticulata</em> Blanco. and <em>Pyrus communis</em>) and ten intercrops <em>viz </em>maize, rice, french bean, pea, and pumpkin during <em>kharif </em>and potato, cabbage, cauliflower, mustard and onion during <em>rabi</em> season of two consecutive years (2013-2015) was conducted at Dalapchand Science Farm, Krishi Vigyan Kendra (KVK), Kalimpong, West Bengal. The experiment was laid out in randomized block design (RBD) with three replications. The fruit plant grafts were planted at spacing of 10 m x 10 m. The silvi saplings were planted in between the two fruit plants and boundary at spacing of 2.5 m during <em>kharif</em> 2011. The intercrops were grown in the interspaces between the two fruit trees during two consecutive years. Depth wise (0-15 cm, 15-30 cm and 30-60 cm) soil samples were collected from the field twice, once at initial (before intercropping) and next at final (at the end of two years of intercropping) by using screw auger. Results revealed that higher improvement in soil physico-chemical properties at 0-15 cm,15-30 cm and 30-60 cm soil depth recorded <em>viz</em>. bulk density (1.26, 1.34, 1.37 gm^-cm³), water holding capacity (39.44, 35.78, 33.29%), soil pH (5.90, 6.23, 6.34), organic carbon (2.04, 1.07, 0.81%), available N (517, 416, 319 kg ha^-1), P (14.38,12.18, 9.52 kg ha^-1), and K (535, 349, 289 status kg ha^-1) respectively were found under <em>Alnus nepalensis</em> + <em>Citrus reticulata</em> + pea + mustard plot at the end of two years of study. However, among the different treatment combination, integrating silvi (<em>Alnus nepalensis</em>) and fruit trees (<em>Citrus reticulata</em> Blanco. and <em>Pyrus communis</em>) with intercrops (<em>kharif</em> + <em>rabi)</em> showed significant improvement in soil physico-chemical properties than silvi and fruit trees alone or sole crops plots.

Objective: To assess the effects of the legume (Pueraria phasoeloïdes) on the chemical parameters of the waste rock soils (saprolites) at the Agbaou gold mine, in the center-west of Côte d’Ivoire. Methodology and results: Soil samples were taken using the systematic sampling method at regular intervals of 20 m on the ramps and at 20 cm soil depth, using an auger during two consecutive sampling campaigns (2016-2017 and 2017-2018). The geometric coordinates of the sampling points were obtained using a GPS Garming CSX60 type. A total of 20 composite samples were made from 80 collected soil samples. Chemical analyzes were carried out on soil samples obtained. The results show that the contents of total organic carbon (TOC), total organic nitrogen (Nt), the C: N ratio and the pH values of the soils, under Pueraria phaseoloïdes legume were significantly improved between the ramps and between the two campaigns (p &lt;0.05). Conversely, (CEC, exchangeable bases, (Ca2+, Mg2+ and K+) and phosphorus contents decreased significantly (p &lt;0.001) between the ramps and the two campaigns. This reflects the improving effect of the legume on the chemical parameters of the soils. However, variations in trace element content between ramps and across campaigns did not show any significant improvement (p&gt; 0.05).

Abstract Background Anemia is the most common extraintestinal manifestation in inflammatory bowel disease (IBD) (1). The laboratory evaluation and determination of anemia in IBD remains challenging (2). The aim of this study was to evaluate the burden, risk factors and types of anemia in IBD patients in Crete. Methods This is a cross sectional study where consecutive IBD patients were included. Demographic, clinical and laboratory data [Hemoglobin (Hgb), Ferritin (Fer)] were recorded (based on an updated IBD registry) while serums of consecutive IBD patients were collected and Soluble transferrin receptor (sTFR), sTFR Index and Hepcidin (Hepc) were measured. Results A total of 151 [69 (45.7%) females, 90 (59.6%) with Crohn’s Disease (CD), 34 (22.5%) anemic and 117 (77.5%) non-anemic] were included. Anemic patients were found to be less frequently smokers (P=0.0182), to have shorter IBD duration (P=0.0112) and more often active disease (P=0.0270) compared to non-anemic IBD patients. No other significant differences in clinical and demographic characteristics were found. In addition, they had significantly lower Hgb, MCV [11.6 (10.7-12.4) vs 14.1 (13.3-15), 80.3 (78.4-85.8) vs 90.6 (86.5-94.5) respectively, both P&amp;lt; 0.0001], Ferritin [35.5 (8.2-69) vs 60 (33-112), P=0.0164], and higher RDW, ESR, sTFR [16.2 (14.9- 17.8) vs 14.2 (13.5-15), 27 (12.5-45) vs 9.5 (8.5-15), 1.85 (1.33-2.67) vs 1.22 (1.02-1.52) respectively, all P&amp;lt;0.0001], CRP [0.6 (0.2-2.5) vs 0.3 (0.1-2), P=0.0028] and sTFR Index [1.14 (0.75-3.10) vs 0.68 (0.55-1.03), P=0.0002)]. In terms of risk factors for anemia development younger age (OR 1.04, CI95% 1.02-1.07), smoking (OR 0.22, CI95% 0.06-0.80) and higher ESR (OR 1.04, CI95% 1.02-1.07) were found to be significant in the multivariate analysis. From the anemic patients (N=34), 17 had iron deficiency (IDA) and the rest non-IDA (anemia of chronic disease and mixed). Patients with IDA compared to non-IDA had significantly higher sTFR and sTFR Index while no difference was found in Hepc (Table 1). sTFR &amp;gt;1.68 mg/l had sensitivity of 76.5% and specificity of 73.3% while sTFR Index &amp;gt;1.1365 has sensitivity 82.4% and specificity 86.7% for IDA diagnosis suggesting that sTFR Index is the most accurate index for IDA diagnosis in IBD patients (Figure 1). Conclusion One out of 5 IBD patients have anemia in our cohort. Risk factors for anemia are the age, smoking status and ESR. sTFR and especially sTFR Index could be useful for true IDA diagnosis in IBD patients in the presence of chronic inflammation. References 1.Kulnigg S, Gasche C. Systematic review: managing anemia in Crohn’s disease. Aliment Pharmacol Ther. 2006;24:1507–232 2.Gordon H, Burisch J, Ellul P, Karmiris K, Katsanos K, Allocca M, Bamias G, Barreiro-de Acosta M, Braithwaite T, Greuter T, Harwood C, Juillerat P, Lobaton T, Müller-Ladner U, Noor N, Pellino G, Savarino E, Schramm C, Soriano A, Michael Stein J, Uzzan M, van Rheenen PF, Vavricka SR, Vecchi M, Zuily S, Kucharzik T. ECCO Guidelines on Extraintestinal Manifestations in Inflammatory Bowel Disease. J Crohns Colitis. 2024 Jan 27;18(1):1-37.

SummarySoil and nutrients losses due to soil erosion are detrimental to crop production, especially in the hilly terrains. An experiment was carried out in three consecutive cropping seasons (2012–2015) with four treatments: sole maize; sole maize with plastic mulch; maize and cowpea under plastic mulching; and maize and soybean under plastic mulching in randomized block design (RBD) to assess their impact on productivity, profitability, and resource (rainwater, soil, and NPK nutrients) conservation in the Indian sub-Himalayan region. The plot size was 9 × 8.1 m with 2% slope, and runoff and soil loss were measured using a multi-slot devisor. The results showed that mean runoff decreased from 356 mm in sole maize with plastic mulch plots to 229 mm in maize + cowpea intercropping with plastic mulch, representing a reduction of 36% and corresponding soil loss reduction was 41% (from 9.4 to 5.5 t ha−1). The eroded soil exported a considerable amount of nitrogen (N) (13.2–31.4 kg ha−1), phosphorous (P) (0.5–1.7 kg ha−1), and potassium (K) (9.9–15.6 kg ha−1) and was consistently lower in maize + cowpea intercropping. The maize equivalent yield (MEY) was significantly higher in maize + cowpea with plastic mulch intercropping than the other treatments. These results justify the need to adopt maize with alternate legume intercrops and plastic mulch. This strategy must be done in a way guaranteeing high yield stability to the smallholder farmers of the Indian sub-Himalayan region.

Objective: To assess the effects of the legume (<em>Pueraria phasoelo&iuml;des</em>) on the chemical parameters of the waste rock soils (saprolites) at the Agbaou gold mine, in the center-west of C&ocirc;te d&rsquo;Ivoire. Methodology and results: Soil samples were taken using the systematic sampling method at regular intervals of 20 m on the ramps and at 20 cm soil depth, using an auger during two consecutive sampling campaigns (2016-2017 and 2017-2018). The geometric coordinates of the sampling points were obtained using a GPS Garming CSX60 type. A total of 20 composite samples were made from 80 collected soil samples. Chemical analyzes were carried out on soil samples obtained. The results show that the contents of total organic carbon (TOC), total organic nitrogen (Nt), the C: N ratio and the pH values of the soils, under&nbsp;<em>Pueraria phaseolo&iuml;des</em>&nbsp;legume were significantly improved between the ramps and between the two campaigns (p &lt;0.05). Conversely, (CEC, exchangeable bases, (Ca²⁺, Mg²⁺&nbsp;and K⁺) and phosphorus contents decreased significantly (p &lt;0.001) between the ramps and the two campaigns. This reflects the improving effect of the legume on the chemical parameters of the soils. However, variations in trace element content between ramps and across campaigns did not show any significant improvement (p&gt; 0.05).&nbsp;

Abstract Introduction: Relapsed/refractory (r/r) and secondary acute myeloid leukemia (AML) are associated with poor outcomes and low survival rates, particularly in older individuals. Because there is no standard salvage regimen, the choice of therapy for patients (pts) is often based on institutional experience. The Polish Adult Leukemia group reported high anti-leukemic activity and acceptable toxicity with CLAG±M in r/r AML pts (Wierzbowska et al, Eur J Haematol 2008); however these patients were primarily younger individuals with a median age of 45 years. Jaglal et al (Leuk Res 2014) reported their single institute experience showing that CLAG-M was superior to historical 7+3 for induction of secondary AML pts after prior azanucleoside therapy. Based on these data, we have been utilizing CLAG±M as a standard induction/re-induction strategy for r/r and secondary AML pts at our institute since 2013. Methods: Here we retrospectively reviewed the medical records of 45 consecutive adult pts with secondary or r/r AML who received CLAG±M chemotherapy at Roswell Park Cancer Institute from 2013 to the present. Disease characteristics, clinical response, toxicities, and overall survival were recorded for all patients. Results: Median age was 66 (range 21-77) years. Twenty-six (58%) were male. Twenty-eight (62%) had received prior hypomethylating agents (HMA). Pts had a median of 1 prior AML therapies (range 0-5). Eight pts (18%) had no previous therapy for AML and of these all had secondary AML. The remainder (72%) had r/r AML. Median ECOG performance status was 1 (0-4). Initial WBC count was 1.86 (0.3-190) K/mcL with a mean of 9.53K/mcL. Median marrow blasts were 35% (0-95%). Two pts had extramedullary AML only. Out of 42 evaluable pts, 12 (29%) had a complete remission (CR), 16 (38%) had a complete remission with incomplete count recovery (CRi), and 3 (7%) had a 50% reduction in marrow blast count (partial remission, PR). The CR/CRi rate was 67% with an overall response rate (CR/CRi/PR) of 74%. Median overall survival (OS) was 107 (17-548) days (Figure 1). Fourteen pts (31%) proceeded to allogeneic transplant (BMT). Treatment was overall well tolerated with no unexpected dose-limiting toxicities. The most common toxicity was neutropenic fever, which occurred in 36 pts (80%). Of note, 35 pts received CLAG+M while 10 pts (23%) received CLAG without mitoxantrone due to prior anthracycline exposure or cardiomyopathy. However ORR (78% vs 60%) and median OS (101 vs. 175 days, p=0.18) in CLAG+M vs. CLAG treated pts were not significantly different. There was no difference in response rates or median OS in patients who had/ had not received prior HMA or who had received several prior lines of therapy (0-2 vs. &gt;2). Two-thirds (30 of 45) of pts were ³ 60 years with a median ECOG of 1 (range 0-3). Despite higher percentages of secondary/therapy-related AML and prior HMA use in older pts, outcomes of CLAG+M were similar in both age groups (Table 1). ORR was 72% vs. 77% (p=NS) and median OS was 101 vs. 145 days (p=0.06) in older versus younger pts, respectively. Equal numbers of older and younger pts (33%) underwent subsequent BMT. In older pts receiving CLAG±M, there were no documented cases of neurotoxicity and no increased neutropenic complications. Conclusions: CLAG±M resulted in high clinical responses and prolonged overall survival in pts with secondary and r/r AML with poor risk features, specifically older age (³60 years old) and multiple prior lines of therapy including previous HMA. Unlike other higher dose cytarabine-containing regimens, CLAG±M was well tolerated without significant neurotoxicity. Although larger prospective clinical trials are required to support these findings, overall our results support the use of CLAG±M as a valuable addition to the current armamentarium of salvage regimens for older fit AML patients. Table 1. Outcomes of older ( ³ 60 yrs) vs. younger AML pts treated with CLAG±M Age ³ 60 yrs Age &lt;60 yrs No. of patients N=30 N=15 Median age (yrs) 72 (60-77) 48 (21-59) Prior HM Agents (%) 22/30 (73%) 6/15 (40%) No. of prior therapies (Median) 1 (0-5) 2 (0-5) Secondary/ tAML (%) 18/3 (70%) 2/0 (13%) Complete remission (CR/CRi, %) 8/11 (66%) 4/5 (69%) Overall response rates (ORR) 21 (72%) 10 (77%) Median OS from CLAG±M (days, range, CI) 101 (32-409, 95% CI 90-158) 145 (17-548, 95% CI 103-295) Neutropenic fever (%) 21/30 (70%) 13/15 (87%) Post treatment BMT (%) 10 (33%) 5 (33%) Figure 1. Survival of CLAG±M patients from treatment Figure 1. Survival of CLAG±M patients from treatment Disclosures Thompson: Kinex Pharmaceuticals: Research Funding. Griffiths:Celgene: Honoraria; Astex: Research Funding; Alexion Pharmaceuticals: Honoraria. Wang:Immunogen: Research Funding.

ABSTRAKDewasa ini kesadaran diri untuk menjaga kesehatan dan kecantikan kulit semakin meningkat. Hal tersebut menyebabkan kosmetik menjadi salah satu produk yang dibutuhkan oleh masyarakat luas dan telah menjadi tren. Experiential quality merupakan faktor penting untuk menciptakan experiential value yang baik. Apabila kedua hal tersebut dirasa baik oleh pelanggan, maka akan timbul niat membeli ulang dan merekomendasikan produk tersebut kepada orang lain. Tujuan dilakukan penelitian ini adalah untuk mengetahui bagaimana pengaruh experiential quality pada behavioral intention dengan experiential value sebagai variabel intervening pada kosmetik halal Golden Viera. Penelitian menggunakan metode kuantitatif dan data yang digunakan dalam penelitian diperoleh dengan cara membagikan kuesioner dengan skala Likert. Teknik purposive sampling digunakan untuk proses pengambilan sampel dengan jumlah sampel sebanyak 50 orang. Kriteria sampel untuk penelitian ini adalah Muslimah yang pernah membeli produk Golden Viera dan pernah menggunakan produk Golden Viera minimal 30 hari berturut-turut. Teknik analisis data menggunakan path analysis. Hasil penelitian ini menunjukkan bahwa experiential quality berpengaruh positif dan signifikan terhadap experiential value dan behavioral intention dan experiential value berpengaruh positif dan signifikan terhadap behavioral intention.Kata Kunci: Experiential Quality, Experiential Value, Behavioral Intention, Kosmetik Halal. ABSTRACTNowadays self-awareness to maintain skin health and beauty is increasing. This causes cosmetics to become one of the products needed by the wider community and has become a trend. Experiential quality is an important factor to create good experiential value. If both of these things are considered good by the customer, then there will be an intention to repurchase and recommend the product to others. The purpose of this study was to find out how the effect of experiential quality on behavioral intention with experiential value as an intervening variable in Golden Viera halal cosmetics. The study used quantitative methods and the data used in the study were obtained by distributing questionnaires with a Likert scale. Purposive sampling technique was used for the sampling process with a total sample of 50 people. The sample criteria for this study were Muslim women who had purchased Golden Viera products and had used Golden Viera products for at least 30 consecutive days. The data analysis technique used path analysis. The results of this study indicate that experiential quality has a positive and significant effect on experiential value and behavioral intention and experiential value has a positive and significant effect on behavioral intention.Keywords: Experiential Quality, Experiential Value, Behavioral Intention, Halal Cosmetics. DAFTAR PUSTAKAAhyar, H., Maret, U. 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Starting from growth that supports development, in the end growth and development go hand in hand. An important period in a child's growth and development begins in infancy because basic growth is what will influence and determine the child's subsequent development. The aim of this research is to detect deviations in the development of early childhood children aged 2-3 years at the ECCE Rahmah El Yunusiyyah Padang Panjang through the Stimulation, Detection and Early Intervention of Child Growth and Development (SDICGD) instruments in the Android feature. This research was conducted using a cross-sectional approach. Participants in this study were 26 children aged 2-3 years using a consecutive sampling technique of 10 children whose growth and development were monitored using the SDICGD android application. The results of this study showed that several partisipants experienced malnutrition, one partisipant out of nine normal partisipants. The Developmental Pre-Screening Questionnaire (DPSQ) instrument of the ten child participants contained nine children (90%) who were according to the developmental stage aged 24-36 months, and one child was not according to the developmental stage. The results of the Attention Deficit and Hyperactivity Disorder (ADHD) test showed that three children (60%) were normal, and two children (40%) were hyperactive. Early detection of children's growth and development must be carried out regularly every month, and according to the child's age. For further research, it is hoped that early detection will also be carried out on the development of children's mental health, not just growth and development which is common and widely researched. Schools and parents must play an active role in children's growth and development so that no developmental stages are missed, and children grow and develop according to their age. Keywords: simulation, detection, early intervention, child growth and development, development of children aged 2-3 years References: Arinny, L. (2023). Deteksi Dini Masalah Perilaku Psikososial Pada Remaja Di Sekolah Menengah Atas Kota Semarang. Jurnal Keperawatan Jiwa (JKJ): Persatuan Perawat Nasional Indonesia, 12(1), 67–74. https://stikes-nhm.e-journal.id/NU/article/view/1749 Dunkel, Luque, Loche, &amp; Savage. (2021) ‘Digital technologies to improve the precision of pediatric growth disorder diagnosis and management’, Growth Hormone and IGF Research, 59, p. 101408. https://doi.org/10.1016/j.ghir.2021.101408. Endo, D. (2014). Monitoring the Growth and Development of Toddlers Using Ma-ternal and Child Health Book. Kesmasindo, Volume 6 N, 166–175. Fitriani, I. S., &amp; Oktobriariani, R. R. (2017). Stimulasi, Deteksi dan Intervensi Dini Orang Tua terhadap Pencegahan Penyimpangan Pertumbuhan dan Perkembangan Anak Balita. Indonesian Journal for Health Sciences, 1(1), 1. https://doi.org/10.24269/ijhs.v1i1.383 Friska, E. and Andriani, H. (2022) ‘The Utilization of Android-Based Application as a Stunting Prevention E-Counseling Program Innovation during Covid-19 Pandemic’, Journal of Maternal and Child Health, 6(5), pp. 323–332. https://doi.org/10.26911/thejmch.2021.06.05.02. González-Pérez, Matey-Sanz, Granell, Díaz-Sanahuja, Bretón-López, &amp; Casteleyn. (2023) ‘AwarNS: A framework for developing context-aware reactive mobile applications for health and mental health’, Journal of Biomedical Informatics, 141(October 2022), p.104359. https://doi.org/10.1016/j.jbi.2023.104359. Gusvita, Y. (2024). Program PAUD Rahmah El Yunusiyyah. Hibana, H., &amp; Surahman, S. (2021). Optimalisasi Perkembangan Anak Melalui Deteksi Dini Tumbuh Kembang Anak. Qurroti : Jurnal Pendidikan Islam Anak Usia Dini, 3(1), 42–55. https://doi.org/10.36768/qurroti.v3i1.150 IDAI. (2013). Recognizing Common Developmental Delays in Children. http://www.idai.or.id/article/seputar-kesehatan-anak/mengenal-keterlamatan-perkembangan-umum-pada-anak Inggriani, D. M. (2019). “Early Detection of Growth and Development of Children Aged 0-6 Years Based on Android Applications.” STIKES Adila Journal, Volume 1,. Inggriani, D. M., Rinjani, M., &amp; Susanti, R. (2019). Deteksi Dini Tumbuh Kembang Anak Usia 0-6 Tahun Berbasis Aplikasi Android. Wellness And Healthy Magazine, 1(1), 115–124. https://wellness.journalpress.id/wellness/article/download/w1117/65 Kozhevnikov, M. (2007). Cognitive Styles in the Context of Modern Psychology: Toward an Integrated Framework of Cognitive Style. Psychological Bulletin, 133(3), 464–481. https://doi.org/10.1037/0033-2909.133.3.464 Kozier, Erb, Berman, &amp; S. (2015). Nursing Fundamentals Textbook: Concepts, Processes, Practices .: Vol. (7th ed.,. EGC. Langarizadeh, M. et al. (2021) ‘Mobile apps for weight management in children and adolescents; An updated systematic review’, Patient Education and Counseling, 104(9), pp. 2181–2188. https://doi.org/10.1016/j.pec.2021.01.035. Mahyumi Rantina, Dra. Rahmanela, Y. K. N. (2021). Buku Stimulasi Dan Deteksi Dini Tumbuh Kembang Anak (0-6Tahun). EDU Publisher. https://books.google.co.id/books?id=raEJEAAAQBAJ&amp;lpg=PP3&amp;pg=PP1#v=onepage&amp;q&amp;f=false Marwasariaty, M., Sutini, T., &amp; Sulaeman, S. (2019). Pendidikan Kesehatan Menggunakan Media Booklet + Aplikasi SDIDTK Efektif Meningkatkan Kemandirian Keluarga dalam Pemantauan Tumbuh Kembang Balita. Journal of Telenursing (JOTING), 1(2), 236–245. https://doi.org/10.31539/joting.v1i2.853 Nahar, B. et al. (2020) ‘Early childhood development and stunting: Findings from the MAL-ED birth cohort study in Bangladesh’, Maternal and Child Nutrition, 16(1). Available at: https://doi.org/10.1111/mcn.12864. Nesy, A. M., &amp; Pujaningsih, P. (2023). Deteksi Dini Tumbuh Kembang pada Anak Usia Pra Sekolah. Jurnal Obsesi : Jurnal Pendidikan Anak Usia Dini, 7(4), 4682–4689. https://doi.org/10.31004/obsesi.v7i4.4517 Nursalam. (2014). Nursing Care for Infants and Children. Salemba Medika. Pandita, A., Sharma, D., Pandita, D., Pawar, S., Tariq, M., &amp; Kaul, A. (2016). Childhood obesity: prevention is better than cure. Diabetes, metabolic syndrome, and obesity: targets and therapy, 9, 83–89. https://doi.org/10.2147/DMSO.S90783. Patel, A.B. et al. (2019) ‘M-SAKHI—Mobile health solutions to help community providers promote maternal and infant nutrition and health using a community-based cluster randomized controlled trial in rural India: A study protocol’, Maternal and Child Nutrition, 15(4), pp. 1–16. https://doi.org/10.1111/mcn.12850 Rahayu, S. F., Anggeriyane, E., &amp; Mariani, M. (2021). Efforts to Strengthen Stimulation, Detection and Early Development and Development Program (SDIDTK) Through Anthropometric Examination in Preschool Children. Jurnal EMPATI (Edukasi Masyarakat, Pengabdian Dan Bakti), 2(1), 71. https://doi.org/10.26753/empati.v2i1.522 Roba, A.A. et al. (2021) ‘Prevalence and determinants of concurrent wasting and stunting and other indicators of malnutrition among children 6–59 months old in Kersa, Ethiopia’, Maternal and Child Nutrition, 17(3), pp. 1–12. https://doi.org/10.1111/mcn.13172. Sari, K. and Sartika, R.A.D. (2021) ‘The effect of the physical factors of parents and children on stunting at birth among newborns in Indonesia’, Journal of Preventive Medicine and Public Health, 54(5), pp. 309–316. https://doi.org/10.3961/jpmph.21.120. SDIDTK. (2016). Pedoman Pelaksanaan Stimulasi, Deteksi dan lntervensi Dini Tumbuh Kembang Anak. Direktorat Kesehatan Departmen Kesehatan Keluarga, 59. Shofiyati, et al. (2022). The Role of Teachers in Online Learning for Early Childhood Children in the Covid-19 Pandemic Era. Golden Generation: Journal of Ear-Ly Childhood Islamic Education., Vol. 5 No.https://journal.uir.ac.id/index.php/generationemas/article/view/8891 Shrestha, M.L. et al. (2022) ‘Malnutrition matters: Association of stunting and underweight with early childhood development indicators in Nepal’, Maternal and Child Nutrition, 18(2), pp. 1–9. https://doi.org/10.1111/mcn.13321. Soetjiningsih. (2014). Child Development. EGC. Suharsimi Arikunto. (2014). Prosedur Penelitian Suatu Pendekatan Praktik. Rineka Cipta. Suprayitno, E., Yasin, Z., Kurniati, D., &amp; Rasyidah. (2021). Peran Keluarga Berhubungan dengan Tumbuh Kembang Anak Usia Pra Sekolah. Journal of Health Science, VI(II), 63–68. Tanuwijaya, S. (2014). General Concept of Growth and Development. EGC. Vanderloo, L.M. et al. (2021) ‘Selecting and evaluating mobile health apps for the healthy life trajectories initiative: Development of the eHealth resource checklist’, JMIR m Health and uHealth, 9(12), pp. 1–8. https://doi.org/10.2196/27533. Wahyudin, T. E. (2021). Handbook for Stimulation and Detection of Child Growth and Development (0-6 Years). EDU Publisher. Wahyuni, T. (2019). Diagnostic Test of the Mother Cares Application (Moca) for Early Detection of the Risk of Developmental Deviations in Toddlers. Unsika Journal, Vol 4 No 1. Winda Windiyani, Sri Wahyuni, E. N. P. (2020). STIMULASI DETEKSI INTERVENSI DINI TUMBUH KEMBANG ANAK. EDU Publisher. Wulandari, U. R., Budihastuti, U. R., &amp; Poncorini, E. P. (2017). Analysis of Life-Course Factors Influencing Growth and Development in Children under 3 Years Old of Early Marriage Women in Kediri. Journal of Maternal and Child Health, 02(02), 137–149. https://doi.org/10.26911/thejmch.2017.02.02.05

Background:Connective tissue disease (CTD) associated pulmonary arterial hypertension (PAH) is considered to be an indication for immunosuppressive therapy (IT) except scleroderma associated PAH. However, the response rate defined by improvement of WHO functional class and hemodynamic parameters is reported to be around 50% [1]. Since CTDs are systemic diseases, it may be difficult to evaluate the efficacy of IT by subjective symptoms. Although there are previous studies reporting that the combined use of IT and pulmonary vasodilators significantly improved hemodynamics [2], response to IT without titration of pulmonary vasodilators remains to be elucidated.Objectives:To examine whether IT is effective for CTD-PAH.Methods:We retrospectively examined the medical records of consecutive 13 patients with CTD-PAH (female 13, mean age 47 ± 15 years) treated with methylprednisolone (1 mg/kg/day, oral) and intravenous bolus cyclophosphamide (IVCY) (500 mg/m2) every four weeks for six times. Patient characteristics are described in Table 1. Right heart catheterization (RHC) was done at prior to IT, before adding PAH specific agents, and at the fifth or sixth course of IVCY. In treated cases, the previous vasodilators remained unchanged during the first term of IT.Results:At the first follow up RHC, decrease of mean pulmonary arterial pressure over 5 mmHg was observed in all patients, and decrease of pulmonary vascular resistance (PVR) was observed in twelve out of 13 patients (Figure 1). Over 20% of PVR reduction was observed more in the patients of pulmonary vasodilator naïve and started IT within one year from symptoms than others (6/7 vs 1/6, p=0.03). Although six-minutes walk distance (6MWD) tended to be prolonged between first and second RHC (298 ± 70 m vs 382 ± 81 m; p=0.054; n = 9), 6MWD was shortened in some cases with good hemodynamic improvement (2/5). All patients were prescribed oral PAH specific agents finally, but no one needed parenteral prostanoids. Two patients (15%) died during maintenance therapy for causes other than PAH. Three-year and five-year survival rates were 91.7% and 81.5%, respectively.Conclusion:IT without titration of pulmonary vasodilators significantly improved hemodynamic parameters despite of less improvement in 6MWD in CTD-PAH patients. Considering that CTDs itself might affect the exercise tolerance regardless of PAH, these hemodynamic changes may contribute to better prognosis and IT might be considered especially for patients early in clinical courses and treatment naïve.References:[1]Jais X, Launay D, Yaici A, et al. Immunosupressive therapy in lupus-and mixed connective tissue disease-associated pulmonary arterial hypertension. ARTHRITIS RHEUM. 2008; 58(2): 521-531.[2]Yamamoto M S, Fukumoto Y, Sugimura K, et al. Intensive immunosuppressive therapy improves pulmonary hemodynamics and long-term prognosis in patients with pulmonary arterial hypertension associated with connective tissue diseasae. Circ J. 2011; 75: 2668-2674.Table 1.Characteristics of patientsPatientAge,yrConnective Tissue DiseaseYears from symptom to immunosuppressive therapyPrevious vasodilatorsvasodilators at final visit147SS1.5PGI2ERA262SS, RA2nonePDE5332SS1noneERA457SS, SSc0.5nonePDE5526SS,MCTD, SLE,SSc0.5nonePDE5670SSc, SS s/o13sGC, ERAsGC, ERA732SS s/o, SLE0.1nonePDE5831MCTD3ERA,PDE5, PGI2ERA,PDE5, PGI2943SSc, SLE0.6ERA, PDE5ERA,PDE5, PGI21067MCTD,PM0nonesGC1141SS0.1noneERA, PDE51269SS0.3nonePDE51344SS, MCTD s/o, SLE s/o0.1noneERA, sGCN.A, not acquired; s/o, suspect of; SS, Sjögren’s syndrome; RA, rheumatoid arthritis; SSc systemic sclerosis; SLE, systemic lupus erythematosus; MCTD, mixed connective tissue disease; PM, Polymyositis; PGI2, prostacyclin derivative; sGC, soluble guanylate cyclase stimulator; ERA, endothelin receptor antagonist; PDE5, phosphodiesterase type 5 inhibitor.Figure 1.Hemodynamic changes during immunosuppressive therapyDisclosure of Interests:Risa Kishikawa: None declared, Masaru Hatano Speakers bureau: Janssen Pharmaceutical K.K, Bayer Yakuhin, Ltd., Grant/research support from: Janssen Pharmaceutical K.K, Nippon Shinyaku Co., Ltd., MOCHIDA PHARMACEUTICAL CO., LTD., Satoshi Ishii: None declared, Mai Shimbo: None declared, Akihito Saito: None declared, Shun Minatsuki: None declared, Yukiko Iwasaki: None declared, Keishi Fujio Speakers bureau: Tanabe Mitsubishi, Bristol Myers, Eli Lilly, Chugai, Jansen, Pfizer, Ono, AbbVie, Ayumi, Astellas, Sanofi, Novartis, Daiichi Sankyo, Eisai, Asahi Kasei, Japan Blood Products Organization, and Kowa, Grant/research support from: Tanabe Mitsubishi, Bristol Myers, Eli Lilly, Chugai, AbbVie, Ayumi, Astellas, Sanofi, Eisai, Tsumura &amp; Co., and Asahi Kasei., Issei Komuro Speakers bureau: AstraZeneka, Daiichi Sankyo Company, Limited, Takeda Pharmaceutical Company Limited, Bayer Yakuhin, Ltd, Pfizer Japan Inc., and Ono Pharmaceutical Co., Ltd., Grant/research support from: Daiichi Sankyo Company, Ltd, Sumitomo Dainippon Pharma Co., Ltd., Takeda Pharmaceutical Company Ltd, Mitsubishi Tanabe Pharma Corporation, Teijin Pharma Limited, Idorsia Pharmaceuticals Ltd, Otsuka Pharmaceutical Co., Ltd., Bayer Yakuhin, Ltd. Ono Pharmaceutical Co., Ltd. Toa Eiyo Ltd

Objective: To assess the relationship between Helicobacter pylori (Hp) infection and primary open-angle glaucoma (POAG); and meantime, to explore the possible mechanism of POAG induced by Hp. Methods: 30 consecutive POAG patients, 30 primary angle-closure glaucoma (PACG) and cataract patients were recruited and divided into three groups according to different diseases. The sera and aqueous humor samples were collected and used to detect Hp-specific IgG antibody (Hp-Ab) with dot immunogold filtration assay (DIGFA). 14C-urea breath test (14C-UBT) was carried out to detect Hp infection of all participants. Results: The Hp-Ab positive rate respectively was 76.7% (23/30) and 66.7% in sera samples and aqueous humor samples for POAG group, which was significantly higher than the corresponding data of the other two groups (all P&lt;0.05). In 14C-UBT, the Hp-Ab positive rate was 63.3% in POAG group and it was close to that of serological result detected by DIGFA (P&gt;0.05). There were little numbers of positive ANA and ENA in the three groups and no meaning to make statistically analysis. Conclusions: There is positive association between Hp infection and POAG, and the autoimmune is suggested as one of the key mechanisms in our opinions.&#x0D; Introduction&#x0D; Glaucoma is one of the commonest causes for blindness in the world. Generally, glaucoma is divided into primary open-angle glaucoma (POAG) and primary angle-closure glaucoma (PACG).1 As a leading causes for blindness, the study of POAG causes more and more attention.2,3To our understand, POAG is a chronic optic neuropathy characterized by atrophy and increased cupping of optic disk. To date, many aspects of its pathogenesis remain unknown but some significant risk factors are advanced age, African origin, familial history of glaucoma and elevated intraocular pressure.4,5&#x0D; Helicobacter pylori (Hp) is a Gram-negative and microaerophilic bacterium which plays an important role in the development of various upper gastrointestinal diseases. With the development of studies, some researchers reported that Hp was also associated with some extragastric diseases, such as ischemic heart disease,6 iron-deficient anemia,7 diabetes mellitus,8 and so on. In 2001, Kountouras et al9 established a higher prevalence of Hp infection in the sera of patients with POAG in a Greek population, and suggested a possible causal link between Hp and glaucoma. Subsequently, this finding was evidenced by some scholars in their own studies.10 But the significance of such an association remains uncertain because of the conflicting findings reported by various studies.11-13 Aiming to such a discrepancy, further studies are necessary.14&#x0D; In this study, we just do detect Hp-specific IgG antibodies (Hp-Ab) in the sera and aqueous humor of patients with different ocular diseases, including POAG, PACG and cataract, and attempt to further determine the relationship between Hp infection and POAG and to analyze the possible mechanism of POAG induced by Hp.&#x0D; Abbreviations&#x0D; ANA, antinuclear antibody; ENA, Extractable nuclear antigen; DIGFA, dot immunogold filtration assay; Hp, Helicobacter pylori; Hp-Ab, Hp-specific IgG antibodies; PACG, primary angle-closure glaucoma; POAG, primary open-angle glaucoma; 14C-UBT: 14C-urea breath test.&#x0D; &#x0D; Subjectsand methods&#x0D; Subjects&#x0D; 30 consecutive POAG patients were enrolled with the average age of 68±7.3 y (ranged from 47 to 78 y). The ratio of the male and the female was 11: 19. Meantime, 30 PACG patients and 30 cataract patients were also recruited, and who were matched by age and sex with the POAG patients. According to different diseases, the participants were divided into POAG, PACG and cataract groups, respectively. All of them were excluded from tumor, immunodeficiency, autoimmune and infectious diseases in clinic, and also had no antibiotics and other medicines related to immunopotentiator or immunosuppressive agents in the six months before the experiment. Written informed consents were obtained from all the participants. The study was approved by the local ethics committee.&#x0D; Hp-Ab detection of sera samples&#x0D; 2 ml venous blood was collected from each of the participants. The serum was obtained after centrifugation and used to detect Hp-Ab with dot immunogold filtration assay (DIGFA) according to the manufacturer’s instruction of the reagent kit (MP Biomedicals Asia-Pacific Pte. Ltd., Singapore).&#x0D; Hp-Ab detection of aqueous humor samples&#x0D; About 50 μl aqueous humor sample was aspirated at the beginning of glaucoma surgery from the each of the patients in the three groups, respectively. Hp-Ab was assayed with DIGFA as same as the detection process of venous blood samples.&#x0D; Detection of Hp infection with 14C-urea breath test&#x0D; Referring to Tang’s report,1514C-urea breath test (14C-UBT) was carried out in POAG group with Hp detection instrument-YH04 (Yanghe Medical Equipment Co. Ltd., China).&#x0D; Sera auto-antibodies detection&#x0D; Serum antinuclear antibody (ANA) was detected with the indirect immunofluorescence assay by a commercialized ANA kit. Extractable nuclear antigen (ENA) was assayed with line immunoassay. All reagents were bought from Jiangsu HOB Biotech Group, China.&#x0D; Statistic analysis&#x0D; Using T-test and Chi-square test, all analyses were performed with SPSS 13.0 software. P value less than 0.05 were considered significant.&#x0D; Results&#x0D; 3.1 Hp infection detection in sera and aqueous humor &#x0D; Of the sera samples, there were 23 cases exhibited Hp-Ab-positive in POAG group, and the positive rate was 76.7% which was significantly higher than those of PACG and cataract group (43.3% and 36.6% respectively). In the aqueous humor samples, there were 18 patients with positive Hp-Ab in POAG group, and the positive rate was 66.7%. Compared to each data of the other two groups, the difference was statistically significant (Table 1). In POAG group, the mean positive rate of sera samples was similar to that of aqueous humor and no difference existed between them (P = 0.287).&#x0D; Table 1. The serum and aqueous humor qualitative test results of the patients with glaucoma&#x0D; Hp infection detection with 14C-UBTAH: aqueous humor; a: POAG group vs cataract group; b: POAG group vs PACG group; c: PACG group vs cataract group.&#x0D; In 14C-UBT, there were 19 patients with Hp-Ab-positive, and the positive rate was 63.3%. Compared to the data detected with DIGFA, the difference was not significant (Table 2).&#x0D; Table 2. Comparison of DIGFA and 14C-UBT for diagnosis of Hp infection in POAG group&#x0D; ANA and ENA detection* represents comparison of the positive rate detected with the two methods.&#x0D; There were 4, 2 and 1 patients with ANA-positive in POAG, PACG and cataract group, respectively. The positive ENA in POAG group were SSA, SSB and Ro-52, and the corresponding numbers were 2, 2 and 1. Only Ro-52 showedpositive in PACG group while there was no positive ENA in cataract group (Table 3).&#x0D; Table 3. The results for sera ANA, ENA of the patients of each group&#x0D; Discussion&#x0D; In Greece, a very active research group led by J. Kountouras published several original contributions as well as the reviews concerning the connection between Hp infection and POAG.14,16 In other counties, there were also several papers containing the similar arguments issued, such as India,17 Turkey,18 Korea19 and so on. In China, Hong et al20 detected Hp infection and POAG through 13C-UBT, and also found the positive correlation between them. Since then, there was no relative article issued by Chinese could be found in PubMed and other well-known scientific database. In this study, referring to other researchers’ reports, we designed and carried out the experiments. In the results, we found that the positive rate of sera Hp-Ab was high to 76.7% in POAG patients, which was significantly higher than those of the other two groups. This finding was close to the data of the previous reports2,21 and further verified that there was a positive relation between Hp infection and POAG.&#x0D; In the present study, we also assayed Hp infection with 14C-UBT. Encouragingly, the positive rate of Hp infection was 63.3%, which was very close to 76.7% detected with DIGFA. This result further indicated the existence of the relation between Hp infection and POAG. However, Bagnis et al22 thought that the studies based on Hp serological assessment might be misleading, since serum antibodies were not the sensitive markers of active Hp infection; while 13C-UBT could clarify the actual prevalence of POAG among patients infected by Hp. In fact, there were still deficiencies for 13C- or 14C -UBT, because it was more suitable for the detection of gastrointestinal Hp infection, and to an extent, there were false-negatives in the test.23 This probably was the just reason for what the positive rate in DIGFA was little higher than that in 14C-UBT in this study. As to the cresyl fast violet staining on the histology preparations of tissue samples of trabeculum and iris introduced by Zavos et al,24 although it could provide the direct and strong evidence for Hp infection in the pathophysiology of POAG, the difficult harvest of the sample limited its application. Therefore, in our opinions, the serological assay is suitable to detect Hp infectionand used to assess the relationship between Hp prevalence and POAG.&#x0D; Except for detecting sera Hp-Ab, we also detected Hp-Ab in the aqueous humor collected from the majority of participants. As the results shown, the positive rate of the POAG group was statistically higher than each of the other groups, respectively. This result was consistent with that of the serological assessment and again showed the positive relation between Hp infection and POAG. However, in another similar study, Deshpande et al17 also found a statistically significant difference between the POAG patients and the controls in the concentration of serum Hp-Ab, but they did not find any significant correlations between the Hp concentrations of the aqueous humor of the different patient groups. This disagreement probably associated with the damage degree of blood-brain barrier (BBB), because the sera Hp-Ab could reach the trabeculum and iris under the condition of the BBB disruption.25 According to the results of the present study, we supported the hypothesis related to POAG onset that Hp-Ab in circulation might get through the blood-aqueous humor barrier, further condensed in aqueous humor and finally induced or aggravated glaucomatous damage.2&#x0D; As to the occurrence of POAG, we thought another autoimmune mechanism was most probable and should not be ignored: Hp infection initiated autoimmune response because of the common genetic components shared in Hp and human nerve tissue; and then, cell destruction which mediated by apoptosis direct caused glaucoma.26 Just based on the theory, we designed and detected sera ANA and ENA of the POAG patients and the control participants, and hoped to find any evidences related to autoimmune. As a result, we found that the positive rate of every group was rather low and there was no difference between them. However, this seronegative result can’t deny the hypothesis of autoimmune mechanism in POAG; and the auto-antibodies specific to eyes, such as trabeculum and iris, were suggested to be detected in future study in our opinions.&#x0D; Conclusion&#x0D; The positive association between Hp infection and POAG not only using serum sample but also aqueous humor sample is found in this study. And further, through the experimental data, it is suggested that the autoimmune induced by Hp infection probably is the key mechanism for POAG onset, and Hp detection should be taken as a routinized index applied to the prevention and therapy of POAG in clinic. However, we can not sufficiently investigate the possible mechanism of POAG relates to Hp infection. Is it true that Hp infection only relative to POAG but not a causative factor for POAG?18 What are the initial mechanisms of Hp in POAG if the pathogen takes part in the onset of the disease? Such questions will be the study topics to the medical researchers worldwide in future.&#x0D; Funding&#x0D; This work is supported by the Research Fund for Lin He’s Academician Workstation of New Medicine and Clinical Translation in Jining Medical University(JYHL2018FMS08), and the Project of scientific research support fund for teachers of Jining Medical University (JYFC2018FKJ023).&#x0D; Conflicts of interest&#x0D; There is no any conflict of interest between all of the authors.&#x0D; References:&#x0D; &#x0D; Chan H. H.; Ng Y.F.; Chu P. H. Clin Exp Optom. 2011, 94, 247.&#x0D; Kountouras J.; Mylopoulos N.; Konstas A. G.; Zavos C.; Chatzopoulos D.; Boukla A. Graefe’s Arch Clin Exp Ophthalmo. 2003, l241, 884.&#x0D; Kim E. C.; Park S. H.; Kim M. S. A. J. Pharmacol. 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<strong>ABSTRACT</strong> <strong>Background:</strong> Impairment of cerebrovascular autoregulation is considered one of the most important mechanisms leading to cerebral hypo- or hyperperfusion in haemodynamically unstable septic patients. That may lead to Sepsis-associated delirium (SAD) which increases morbidity and mortality.&nbsp; Objective: To investigate the ability of Trans cranial Doppler (TCD) for prediction of delirium in septic patient and its relationship with jagular venous oxygen saturation (JVo2) levels. <strong>Method:</strong> On the first day we used a 3-MHz Tran&rsquo;s cranial Doppler&nbsp;&nbsp; probe to measure the Blood velocity and Pulsatility index in the middle cerebral artery (VMCA) TCD was then repeated daily for 3 consecutive days. Simultaneously we measured r jugular venous oxygen saturation (JVO2) on the same side of the highest VMCA.&nbsp; Confusion Assessment Method for the Intensive Care Unit (CAM-ICU) was done for each patient once per day throughout ICU stay and after 6 hours after stoppage of sedation in sedated patient. <strong>Results:</strong> Out of 159 patients, 91 developed delirium. APACHE score was higher in the delirium group. Patients who developed delirium had significantly longer ICU LOS 13.9 day&rsquo;s vs 7.8 Delirium group had lower mean MCA velocity&nbsp; and higher pulsatility index at all times .Positive correlation was observed between Jvo2 and VMCA on day 2 (r=0.8), and on day 3 (r=0.69). There was a negative correlation between PI and JVo2 on day 2(r= -0.5) and day 3(r=-o.57). Roc curve analyses the ability to detect delirium with a cut off value for Jvo2 measured at day 3(Jvo2 3) of 53.5 % (sensitivity 100%, specificity 100%, P &lt;0.05), and a cut off value for the PI at day 3 (PI3) of 1.2. (AUC= 0.88, CI 95%, 0.83-0.9 P &lt;0.05vsensitivity 70%, specificity 100%). <strong>Conclusion:</strong> Changes in TCD findings together with JVo2 levels are associated with the development of delirium in septic patients. <strong>Key words:</strong>&nbsp; Transcranial Doppler, Sepsis, Delirium, Sepsis, Jugular venous oxygen saturation. <strong>REFERENCES</strong> Pytel P, Alexander J J. Pathogenesis of septic encephalopathy.Curr Opinoin Neurology. 2009; 22:283&ndash;287. Papadopoulos MC, Davies DC, Moss RF, Tighe D, Bennett E. Pathophysiology of septic encephalopathy, a review<em>. Crit Care Med</em>. 2000; 28:3019&ndash;3024. Nagaratnam N, Brakoulias V, Ng .Multiple cerebral infarcts following septic shock. <em>J ClinNeurosci</em>. 2002; 9:473&ndash;476. Rosengarten B, Wolff S, Klatt S, Schermuly RT. Effects of inducible nitric oxide synthase inhibition or norepinephrine on the neurovascular coupling in an endotoxic rat shock model<em>. Crit Care</em>. 2009;3(4):R139. Mihaylova S, Killian A, Mayer K, Pullamsetti SS, Schermuly R, Rosengarten B. Effects of anti-inflammatory vagus nerve stimulation on the cerebral microcirculation in endotoxinemic rats. <em>J Neuroinflammation.</em> 2012;3:183. Sharshar T, Polito A, Checinski A, Stevens RD. Septic-associated encephalopathy&ndash;everything starts at a microlevel<em>. Crit Care</em>. 2010;3(5):199. Bowton DL, Bertels NH, Prough DS, Stump DA. Cerebral blood flow is reduced in patients with sepsis syndrome. <em>Crit Care Med</em>. 1989;3(5):399&ndash;403 Sharshar T, Carlier R,et al.. Brain lesions in septic shock: a magnetic resonance imaging study. <em>Intensive Care Med</em>. 2007;3(5):798&ndash;806 F&uuml;lesdi B, Szatm&aacute;ri S, et al. Cerebral vasoreactivity to acetazolamide is not impaired in patients with severe sepsis. <em>J Crit Care</em>. 2012;3(4):337&ndash;343. Szatm&aacute;ri S, V&eacute;gh T, Csom&oacute;s A, Hallay J, Tak&aacute;cs I, Moln&aacute;r C, F&uuml;lesdi B. Impaired cerebrovascular reactivity in sepsis-associated encephalopathy studied by acetazolamide test. <em>Crit Care.</em> 2010;3(2):R50. Bowie RA, O&rsquo;Connor PJ, Mahajan RP. Cerebrovascular reactivity to carbon dioxide in sepsis syndrome.Anaesthesia. 2003;3(3):261&ndash;265. Matta BF, Stow PJ. Sepsis-induced vasoparalysis does not involve the cerebral vasculature: indirect evidence from autoregulation and carbon dioxide reactivity studies. <em>Br J Anaesth</em>. 1996;3(6):790&ndash;794. Taccone FS, Castanares-Zapatero D, Peres-Bota D, Vincent JL, Berre&rsquo; J, Melot C. Cerebral autoregulation is influenced by carbon dioxide levels in patients with septic shock. <em>Neurocrit Care.</em> 2010;3(1):35&ndash;42. Rosengarten B, Krekel D, Kuhnert S, Schulz R. Early neurovascular uncoupling in the brain during community acquired pneumonia<em>. Crit Care</em>. 2012;3(2):R64. Szatm&aacute;ri S, V&eacute;gh T, Csom&oacute;s A, Hallay J, Tak&aacute;cs I, Moln&aacute;r C, F&uuml;lesdi B. Impaired cerebrovascular reactivity in sepsis-associated encephalopathy studied by acetazolamide test. <em>Crit Care</em>. 2010;14:R50. Pierrakos C, Antoine A, Velissaris D, Michaux I, Bulpa P, Evrard P, Ossemann M, Dive A. Transcranial doppler assessment of cerebral perfusion in critically ill septic patients: a pilot study. <em>Ann Intensive Care</em>. 2013;3:28. Dellinger RP, Levy MM, Rhodes A, et al. Surviving Sepsis Campaign Guidelines Committee Including the Pediatric Subgroup. &nbsp;Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock: 2012.&nbsp;<em>&nbsp;Crit Care Med</em>. 2013;41(2):580-637. Gosling RG, King DH: Arterial assessment by Doppler-shift ultrasound. <em>Proc R Soc Med</em>. 1974, 67: 447-449. Wei LA, Fearing MA, Sternberg EJ, Inouye SK: The confusion assessment method: a systematic review of current usage. <em>J Am Geriatr Soc</em>. 2008, 56: 823-830. Charalampos Pierrakos,&nbsp; RachidAttou, Laurence Decorte, Athanasios Kolyviras, Stefano Malinverni,&nbsp; Philippe Gottignies, Jacques Devriendt, and David De Bels. Transcranial Doppler to assess sepsis-associated encephalopathy in critically ill patients .<em>BMC Anesthesiol</em>.2014; 14: 45. Charalampos Pierrakos, Aur&eacute;lie Antoine, Dimitrios Velissaris, Isabelle Michaux,1 Pierre Bulpa, Patrick Evrard, Michel Ossemann, and Alain Dive. Transcranial doppler assessment of cerebral perfusion in critically ill septic patients: a pilot study. <em>Ann Intensive Care</em>. 2013; 3: 28. Patrick Schramm, Klaus Ulrich Klein, Lena Falkenberg, Manfred Berres,2 Dorothea Closhen, Konrad J Werhahn, Matthias David, Christian Werner, and Kristin Engelhard.Impaired cerebrovascular autoregulation in patients with severe sepsis and sepsis-associated delirium.Crit Care. 2012; 16(5): R181. Sateesh Pujari, &amp; Estari Mamidala. (2015). Anti-diabetic activity of Physagulin-F isolated from Physalis angulata fruits. The American Journal of Science and Medical Research, 1(2), 53&ndash;60. https://doi.org/10.5281/zenodo.7352308 Leslie A. Wei, B.A.,&nbsp;Michael A. Fearing, Ph.D.,&nbsp;Eliezer J. Sternberg,&nbsp;and&nbsp;Sharon K. Inouye, M.D., MPH The Confusion Assessment Method (CAM): A Systematic Review of Current Usage. J Am Geriatr Soc. 2008 May; 56(5): 823&ndash;830.&nbsp; Thees C, Kaiser M, Scholz M, Semmler A, Heneka MT, Baumgarten G, Hoeft A, Putensen C. Cerebral haemodynamics and carbon dioxide reactivity during sepsis syndrome. Crit Care. 2007;16:R123. Szil&aacute;rd Szatm&aacute;ri, Tam&aacute;s V&eacute;gh, &Aacute;kos Csom&oacute;s, Judit Hallay, Istv&aacute;n Tak&aacute;cs, Csilla Moln&aacute;r, and B&eacute;la F&uuml;lesdi. Impaired cerebrovascular reactivity in sepsis-associated encephalopathy studied by acetazolamide test. Crit Care. 2010; 14(2): R50.

BackgroundRecurring cutaneous squamous cell carcinoma (SCC) remains an area of high unmet medical need. While anti-PD-1 antibodies are now approved for this diagnosis, more than half the patients will need more effective treatments, supporting the development of new or combination regimens. Weekly cetuximab targets EGFR and has anti-tumor immunogenic properties that could complement anti-PD-1 immunotherapy. Cetuximab is being evaluated in combination clinical trials. Panitumumab also targets EGFR but is felt to function as a signal transduction inhibitor with weaker anti-tumor immunogenic properties; however, this medication is dosed every two weeks rather than weekly and has a relatively favorable toxicity profile.MethodsTwo consecutive elderly patients with significant comorbidities presented with a performance status of ECOG 3 and rapidly progressive recurrent cutaneous SCC of the face. The patients were presented treatment with an anti-PD-1 antibody, with an option - were there an inadequate palliative response - to include an EGFR antibody provided tolerance was adequate and molecular markets supported so doing. Each patient signed consent for treatment and consent for photographs. Dosing was per package insert, starting conservatively with pembrolizumab 2 mg/kg or nivolumab 3 mg/kg, respectively, escalating in both cases to flat dosing once it was apparent that tolerance was acceptable. The first cycle of panitumumab (6 mg/kg), when needed to be invoked, was administered solo between two cycles of PD-1 inhibitor, then every two weeks while the PD-1 inhibitor continued every two - four weeks.ResultsA 78 year old women with significant cardiac disease and a St Jude tissue aortic valve, had undergone prior surgeries and radiation therapy for her recurring SCC of the face followed then by major resection, parotidectomy, flap reconstruction, and supraomohyoid neck dissection; only two weeks after the latter surgery, she presented with over 20 new in-radiation field metastases (see photo below). A 90 year old woman with emphysema on home oxygen and living in a facility presented with diffuse local recurrence 4 months after orbital exenteration, parotidectomy, neck dissection, and flap. Both patients‘ tumors were characterized: PDL1 (clone E1L3N) 2% and 10%, respectively; scant peritumoral or intratumoral lymphocytes; tumor mutation burden high (33 and 30 mutations per megabase, respectively); epidermal growth factor receptor (EGFR) high 3+ by IHC, but with no gene mutations detected in EGFR, kras or nras; microsatellite stable. In the 78 yo woman, after two cycles of pembrolizumab, the ~ 5 mm pink nodules grew further to up to 3 cm with facial erythema, edema, sealing the eye closed. Only by criteria was this not considered pseudoprogression, Panitumumab was integrated between cycles 2 and 3, resulting in a dramatic abrupt response: the masses became centrally necrotic, flaking, pouring off her face with prompt resolution in edema and complete response (CR) within 2 months - now lasting over 18 months - a period during which pembrolizumab and panitumumab were continued for 27 and 26 cycles respectively). Her major toxicity was diffuse erythema involving ~ 30% of her torso; this resolved early on with triamcinolone 0.1% cream. She also developed scabs in her uninvolved scalp - some where other squamous and basal carcinomas had previously been resected and these all healed slowly (see photo), suggesting we were preventing similar future cancers from emerging in these areas. Similarly, the 90 yo woman achieved only a mixed response to nivolumab over 3 months with shrinking level V neck node but continued stubborn diffuse disease over her face and into the exenteration field. When panitumumab was added, however, there was clear improvement (See photo). With each of eight cycles, prolific crusting/scabbing would occur, shed, and reoccur, some in areas of the face without visible tumor, Mild acneiform rash and mild hypomagnesemia were readily managed. Her performance status and appetite improved and she gained back 14 pounds. After only 6 months, with pathologically confirmed CR, treatment had to be held because she was restricted to her assisted living facility in the midst of the COVID-19 pandemic. Now after a year, the remaining scabs are largely gone (see photo).Abstract 467 Figure 1Panitumumab + pembrolizumab for metastatic cutaneous SCC #1Dramatic durable response in 22 metastases on face and also scabbing then healing on scalp where there was no evidence of tumor but history of prior resected.squamous cell and basal cell carcinomas, suggesting effective prevention of future such lesionsAbstract 467 Figure 2Panitumumab + pembrolizumab for metastatic cutaneous SCC #2Durable response lasting a year after 6 months of treatment in a 90 yo womanConclusionsThe excellent tolerance of multiple cycles of out-patient combination treatment in these two consecutive patients with the same diagnosis, coupled with the observed durable anti-tumor clinical activity lasting now over a year - all support further exploration of panitumumab in combination with anti-PD-1 antibody treatment. A randomized trial would be needed to establish whether outcomes are truly better with the combination. Deciding on hyperprogression v pseudoprogression while getting anti-PD-1 antibody treatment remains a challenge. Laboratory studies would evaluate how such specific signal transduction inhibition by panitumumab might interfere with immune suppressive mechanisms in metastases, rendering them more sensitive to an induced anti-tumor cellular immune response by an anti-PD-1 antibody. Finally such combination treatment should help reduce the need for increasingly cosmetically and functionally altering surgeries.Ethics Approval‘Per our Hartford Health Care IRB, case series of three or less patients does not constitute research.’ConsentWritten informed consent was obtained from the patient for publication of this abstract and any accompanying images. A copy of the written consent is available for review by the Editor of this journal.ReferencesChen A1,2, Ali N3,4, Boasberg P5,6, Ho AS7,8. Clinical Remission of Cutaneous Squamous Cell Carcinoma of the Auricle with Cetuximab and Nivolumab. J Clin Med 2018 Jan 10;7(1). pii: E10.Foote MC, McGrath M, Guminski A, Hughes BG, Meakin J, Thomson D, Zarate D, Simpson F, Porceddu SV Phase II study of single-agent panitumumab in patients with incurable cutaneous squamous cell carcinoma. Ann Oncol 2014 Oct;25(10):2047–52.Ferris RL, Gillison ML, Harris J, et al. Safety evaluation of nivolumab concomitant with cetuximab-radiotherapy for intermediate and high-risk local-regionally advanced head and neck squamous cell carcinoma (HNSCC): RTOG 3504. Oral presentation at: 2018 ASCO Annual Meeting; June 1–5, 2018; Chicago, IL.Jong Chul Park, Lori J. Wirth, Keith Flaherty, Donald P. Lawrence, Shadmehr Demehri, Stefan Kraft, Immune checkpoint inhibition in advanced cutaneous squamous cell carcinoma: Clinical response and correlative biomarker analysis. Journal of Clinical Oncology36, no. 15_suppl (May 20 2018) 9564.FDA approves pembrolizumab for cutaneous squamous cell carcinoma. FDA website. Published June 24, 2020. fda.gov/drugs/drug-approvals-and-databases/fda-approves-pembrolizumab-cutaneous-squamous-cell-carcinoma.Edith Borcoman, MD, Amara Nandikolla, MD, Georgina Long, BSc, PhD, MBBS, FRACP, Sanjay Goel, MD, and Christophe Le Tourneau, MD, PhD. Patterns of Response and Progression to Immunotherapy American Society of Clinical Oncology Educational Book 38 (May 23, 2018) 169–1787.Migden MR, Rischin D, Schmults CD, Guminski A, Hauschild A, Lewis KD, Chung CH, Hernandez-Aya L, Lim AM, Chang ALS, Rabinowits G, Thai AA, Dunn LA, Hughes BGM, Khushalani NI, Modi B, Schadendorf D, Gao B, Seebach F, Li S, Li J, Mathias M, Booth J, Mohan K, Stankevich E, Babiker HM, Brana I, Gil-Martin M, Homsi J, Johnson ML, Moreno V, Niu J, Owonikoko TK, Papadopoulos KP, Yancopoulos GD, Lowy I, Fury MG. PD-1 Blockade with Cemiplimab in Advanced Cutaneous Squamous-Cell Carcinoma. N Engl J Med 2018 Jul 26;379(4):341–351.Eve Maubec, Marouane Boubaya, Peter Petrow, Nicole Basset-Seguin, Jean-Jacques Grob, Brigitte Dreno,. Pembrolizumab as first line therapy in patients with unresectable squamous cell carcinoma of the skin: Interim results of the phase 2 CARSKIN trial. Journal of Clinical Oncology 36, no. 15_suppl (May 20 2018) 9534.Burtness B, et al. First-line pembrolizumab a new standard for recurrent, metastatic head and neck squamous cell carcinoma. Abstract LBA8_PR. Presented at: European Society for Medical Oncology Congress; Oct. 19–23, 2018; Munich. 10. Teruki Yanagi,* Shinya Kitamura, and Hiroo Hata. Novel Therapeutic Targets in Cutaneous Squamous Cell Carcinoma. Front Oncol 2018; 8: 79.

Original Research Paper CONCEALED BURDEN OF UNDERNUTRITION AND OVERNUTRITION AMONG SCHOOL GOING CHILDREN DURING COVID 19 PANDEMIC IN KANYAKUMARI DISTRICT <strong>Authors:</strong> <strong>1Brindha S, 2Steeve Gnana Samuel*, 3Thulasi T*</strong> <em>1. Assistant Professor, Department of Paediatrics, Kanyakumari Government medical college Hospital, Tamilnadu, India.</em> <em>2,3* Resident, Department of Paediatrics, Kanyakumari Government medical college Hospital, Tamilnadu, India.</em> Corresponding author: Steeve Gnana Samuel, Kanyakumari Government Medical College Hospital, <strong>Article Received:</strong>&nbsp; 15-08-2022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <strong>Revised:</strong>&nbsp; 03-09-2022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <strong>Accepted:</strong> 23-09-2022 <strong>ABSTRACT</strong><strong>:</strong> <strong>Objectives:</strong> COVID- 19 pandemic has caused significant disruptions in children&#39;s lifestyles leading to increased burden of undernutrition and overnutrition. This study was designed to document lifestyle behaviour changes in school-going children aged 6 to 12 years of Kanyakumari district during COVID -19 pandemic and to analyze the burden of overnutrition and undernutrition. <strong>Methodology:</strong> This is a Cross-sectional observational study was conducted in Paediatric OPD of Kanyakumari Government Medical college hospital, India. 200 school-going children between the ages of 6 &ndash; 12 were selected using a consecutive sampling technique. A detailed questionnaire about dietary habits and physical activity was formatted. In addition, height and weight measurements were performed, and BMI was calculated. <strong>Results:</strong> The cohort comprised 200 children, of which 111 were females (55.5%) and 89 (44.5%) were males. The cohorts were divided based on age into three groups: 6-8 years (n=92), 9-10 years (n=52), 11-12 years (n=56). 43 children (21.5%) gave a history of consuming fast foods. 64 children (32%) of them engaged in some form of physical activity, while 136 children (68%) gave a history of sedentary lifestyle. One child (0.5%) was underweight, 33 were borderline (16.5%), 153 were normal (76.5%), 8 were overweight (4%), and 5 (2.5%) were obese. A statistical significance relation (P=0.001) was found between fast food and BMI. <strong>Conclusion:</strong> Poor eating habits and sedentary lifestyles established during the COVID-19 pandemic can be difficult for both parents and children to reverse. Childhood is an important time to learn and inculcate healthy eating habits that continue into adulthood. Most notably, malnutrition at a young age can have long-term consequences. The study was able to demonstrate a definite correlation between eating habits and health outcomes in children. <strong><em>Keywords: COVID-19, BMI, Children, nutritional status</em></strong> &nbsp; &nbsp; <strong>INTRODUCTION</strong>: COVID &ndash; 19 pandemic led to unprecedented upheavals around the world. Many countries closed schools and imposed domiciliary confinement to gain control over the pandemic. While countries continued to fight the pandemic, physical and mental health of children and adolescents was given less attention which severely impacted lifestyle behaviours, such as physical activity and sedentary behaviour, with increased consumption of unhealthy fast foods. Low intake of natural or less processed foods and high intake of ultra-processed foods have been associated with negative health consequences, like weight gain, increased body fat, nutritional insufficiency, worsening insulin and lipid profile in people of various ages, including schoolchildren. ^1,2,3The medical community was concerned about the potential health consequences of the COVID-19 on children and adolescents. A study on the indirect impact of the COVID-19 pandemic in low- and middle-income countries noted an increase in the prevalence of undernutrition that would account for 18&ndash;23% of new child fatalities occurring each month.^{2 It} was still unclear how much this epidemic affected children&#39;s nutritional status thus raising the risk of malnutrition, namely obesity and under-nutrition.⁴ &nbsp;There was a lack of data regarding the nutritional impact of COVID-19 on children. In this context, this study was designed to document lifestyle behaviour changes in India&#39;s school-going children in the age group of 6 to 12 years during COVID -19 and investigate the burden of overnutrition and undernutrition in Kanyakumari district. <strong>MATERIAL AND METHODS</strong>:&nbsp; This was a Cross-sectional observational study that was conducted in Paediatric OPD of Kanyakumari medical college hospital, India. Institutional ethical board clearance and informed consent was obtained from parents before commencement of study. The study group consisted of all school-going children between 6 to 12 years of age in the Kanyakumari district. 200 school going children based on consecutive sampling techniques were included in this study. The inclusion criteria were all school-going children between the age group of 6 to 12 years who consented to participate in the study. Children of parents who did not consent, genetic disorders were excluded from the study. The study was conducted from June 2021 to November 2021.&nbsp; The study included two hundred school-going children based on consecutive sampling techniques. A detailed questionnaire of dietary habits and physical activity (PA) was included in the study. Demographic characters of age and gender were noted. Also, the children&#39;s height (centimetre) and weight (kilogram) were measured. Body Mass Index (BMI) was calculated as weight in kilograms divided by the square of the person&#39;s height in metres (kg/m2). Weight status was categorized as underweight for BMI values &lt;5th percentile (BMI-SDS&thinsp;&lt;&thinsp;&minus;1.645), normal for BMI between the 5th and 84th percentiles (&minus;1.645&thinsp;&le;&thinsp;BMI-SDS&thinsp;&le;&thinsp;1.036), overweight for BMI between the 85th and 95th percentiles (1.036&thinsp;&lt;&thinsp;BMI-SDS&thinsp;&le;&thinsp;1.645), and obese for BMI equal to or higher than the 95th percentile (BMI-SDS&thinsp;&gt;&thinsp;1.645).&nbsp; All data were analysed using the Pearson chi-square test in SPSS v21. <strong>RESULTS</strong>: In this study, 200 children were included, 111 were females (55.5%) and 89 (44.5%) were males. Out of 200 children, 46% were in age between 6 to 8 years, 26% were in 9 to 10 years, 28% were in 11 to 12 years. In 200 children, 0.5% were underweight, 4% were overweight and 2.5% obese. 21.5% were taking fast food in their diet. 32% of them engaged in some form of physical activity, while 68% gave a history of a sedentary lifestyle. A statistically significant association was found between fast food and BMI (p=0.001). Among the children who did not eat fast food, 82.8% were had normal weight, and for those who consumed fast food, 16.3% were had increased weight (Table 2). There was no statistically significant association between physical activity and BMI (p=0.093), age group and BMI (p=0.588), age group and fast-food diet (p=0.997), age group and physical activity (p=0.804). &nbsp; <strong>Table </strong><strong>1</strong><strong> Characteristics of Participants:</strong> Participant&rsquo;s characteristics&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; Frequency Percent AGE GROUP 6-8 92 46.0% 9-10 52 26.0% 11-12 56 28.0% <strong>GENDER</strong> FCH 111 55.5% MCH 89 44.5% <strong>BMI</strong> Underweight 1 0.5% Borderline 33 16.5% Normal 153 76.5% Overweight 8 4.0% Obesity 5 2.5% <strong>FAST FOOD</strong> No 157 78.5% Yes 43 21.5% <strong>PHYSICAL ACTIVITY</strong> No 136 68.0% Yes 64 32.0% &nbsp; &nbsp; &nbsp; &nbsp; <strong>Table </strong><strong>2</strong><strong> Association between fast food and BMI</strong> &nbsp; BMI Total P-value Underweight Normal Borderline Overweight Obesity FAST FOOD No Count 1 130 20 3 3 157 0.001 % within FAST FOOD 0.6% 82.8% 12.7% 1.9% 1.9% 100.0% Yes Count 0 23 13 5 2 43 % within FAST FOOD 0.0% 53.5% 30.2% 11.6% 4.7% 100.0% Total Count 1 153 33 8 5 200 % within FAST FOOD 0.5% 76.5% 16.5% 4.0% 2.5% 100.0% &nbsp; <strong>Table </strong><strong>3</strong><strong> Association between physical activity and BMI</strong> &nbsp; BMI Total P-value Underweight Borderline Normal Overweight Obesity PHYSICAL ACTIVITY No Count 1 17 111 5 2 136 0.093 % within PHYSICAL ACTIVITY 0.7% 12.5% 81.6% 3.7% 1.5% 100.0% Yes Count 0 16 42 3 3 64 % within PHYSICAL ACTIVITY 0.0% 25.0% 65.6% 4.7% 4.7% 100.0% Total Count 1 33 153 8 5 200 % within PHYSICAL ACTIVITY 0.5% 16.5% 76.5% 4.0% 2.5% 100.0% &nbsp; <strong>Table </strong><strong>4</strong><strong> Association between age group and BMI</strong> &nbsp; BMI Total P-value Underweight Borderline Normal Overweight Obesity AGE GROUP 6-8 Count 0 16 71 3 2 92 0.588 % within AGE GROUP 0.0% 17.4% 77.2% 3.3% 2.2% 100.0% 9-10 Count 0 8 42 2 0 52 % within AGE GROUP 0.0% 15.4% 80.8% 3.8% 0.0% 100.0% 11-12 Count 1 9 40 3 3 56 % within AGE GROUP 1.8% 16.1% 71.4% 5.4% 5.4% 100.0% Total Count 1 33 153 8 5 200 % within AGE GROUP 0.5% 16.5% 76.5% 4.0% 2.5% 100.0% &nbsp; <strong>Table </strong><strong>5</strong><strong> Association between age group and fast food</strong> &nbsp; FAST FOOD Total P-value No Yes AGE GROUP 6-8 Count 72 20 92 0.997 % within AGE GROUP 78.3% 21.7% 100.0% 9-10 Count 41 11 52 % within AGE GROUP 78.8% 21.2% 100.0% 11-12 Count 44 12 56 % within AGE GROUP 78.6% 21.4% 100.0% Total Count 157 43 200 % within AGE GROUP 78.5% 21.5% 100.0% &nbsp; <strong>Table </strong><strong>6</strong><strong> Association between age group and physical activity</strong> &nbsp; PHYSICAL ACTIVITY Total P-value No Yes AGE GROUP 6-8 Count 61 31 92 0.804 % within AGE GROUP 66.3% 33.7% 100.0% 9-10 Count 35 17 52 % within AGE GROUP 67.3% 32.7% 100.0% 11-12 Count 40 16 56 % within AGE GROUP 71.4% 28.6% 100.0% Total Count 136 64 200 % within AGE GROUP 68.0% 32.0% 100.0% &nbsp; &nbsp; DISCUSSION: COVID-19 was anticipated to worsen all forms of malnutrition around the world, putting the Sustainable Development Goals (SDG) of ending all forms of malnutrition by 2030 in jeopardy. Physical inactivity, sedentariness, and poor diet can all contribute to weight gain. Physical inactivity, sedentary lifestyle patterns, and eating choices are the major factors that determine BMI maintenance and causative of obesity in adolescents and young adults. Alterations in body weight, whether obese or underweight, are significant health-related risk factors for various diseases, including COVID-19.^5,6 This research aimed to examine the relation between lifestyle behaviours in children during COVID-19 their impact on BMI. The results revealed a statistically significant correlation between fast food and BMI, signifying an increase in BMI with fast food consumption. All the other parameters examined were not significant. Different studies on malnutrition during the COVID19 pandemic was analysed. A prospective cohort study in Saudi Arabia evaluated 628 students between 18 and 30 years of age to ascertain if BMI, physical activity, and lifestyle, including diet, sleep, and mental health, changed significantly before and during COVID-19 lockdown. BMI of the students exhibited that 32% had increased, 22% had reduced, and 46% had maintained the same weight during COVID-19 lockdown. The physical activity significantly decreased, and sedentary time increased. The results of the present study were in concurrence with the present study.⁶ An Israel study of 220 paediatric subjects aged between 5 to 18 years measured height, body mass index (BMI) and muscle-to-fat ratio (MFR) z scores and scrutinized how children and adolescents&#39; body composition differed during the pandemic. The results revealed that subjects&#39; weight and body composition were relatively stable. In contrast to the present study, this research found a significant relation between PA and improved body composition^.7 During the COVID-19 school closures, variations in BMI, weight, and height among 19,066&nbsp;Chinese preschool children were noted in an observational retrospective study. Akin to our study, the results of the present study observed no noteworthy variance in the children&#39;s weight change&nbsp;and PA. Childhood obesity rates increased during the COVID-19-related school closures, while preschool children&#39;s BMI reduced the least during the closures compared to pre-COVID-19 periods.⁸ COVID-19 Impact on Lifestyle Change Survey (COINLCS) conducted in China assessed 10,082 participants from high schools, colleges, and graduate schools, aged 19.8&thinsp;&plusmn;&thinsp;2.3 years, before and after COVID-19 lockdown. Dissimilarity of results could be observed between our and COINLICS cohorts where youths&#39; average BMI significantly increased, with the prevalence of overweight/obesity and obesity also increasing, with decreased PA.⁹ Stavridou et al. conducted a literature review of 15 articles to evaluate obesity in children, adolescents and young adults in the course of the COVID-19 pandemic. The researchers noticed increased intake of fried food and sweets, potato, meat and sugary drinks among adolescents and younger age, and higher BMI. Also noted was decreased PA and increased sedentary activity, with weight changes which were linked to limited physical activity. Increased obesity was also noted. A similar significance of BMI and fast food was noted in the present study.¹⁰ The dortmund nutritional and anthropometric longitudinally designed (DONALD) study, Germany, investigated repeated 3-day weighed dietary records from 108 participants (3&ndash;18 years) to see how the pandemic affected nutrients and food intake of children and adolescents. A significantly lower total energy was noted among children and adolescents during the pandemic. BMI and overweight status were comparable before and after the pandemic. Contrarily we found a statistically significant relationship between BMI and fast food.¹¹ Another study was designed to compare and contrast the amount of time Saudi and non-Saudi teenage pupils aged 12 to 18 years spent watching TV, using computers, participating in physical activity, and their food preferences. The connections between these lifestyle behaviours and BMI were investigated. Saudi boys who stated PA 2-5/week, the most time spent watching television and computer, and the highest frequency of consuming fast food and soft drinks had a significantly higher mean BMI than the non-Saudi boys. Similar food habit and BMI association was found in the present study also. ¹² An online questionnaire-based survey involving 1065 individuals in the age group of 13years to 25year evaluated the effect of the COVID 19 pandemic on lifestyle. The results revealed an increase in mean sleeping duration and average screen time, with 38.6% subjects suggesting decreased physical activity levels. 51.9% experienced increased stress levels while 76.4% indicated increased food intake. ¹³ A retrospective cohort study&nbsp;measured body mass index (BMI) from the pre-pandemic and compared with the COVID-19 pandemic period among 36,837 Jewish and Arabic ethnicity in Israel, aged between 2 to 20 years. In line with our results, the Israeli study also found that BMI- standard deviation scores increased significantly in children and adolescents during the pandemic, with an overall increase in the prevalence of obesity by 1.8%. In the pre-pandemic period, 11.2 percent of individuals with normal weight had overweight or obesity; and obesity was present in 21.4 percent of those with overweight in the pre-pandemic period.¹⁴ A COV-EAT cross-sectional online survey study among 397 children/adolescents aged 2&ndash;18 years in Greece documented changes in their families&#39; lifestyle habits, body weight, and sociodemographic data. During the lockdown, sleep duration, as well as screen time, increased, with decreased PA. Bodyweight increased in 35% of subjects and was significantly associated with increased consumption of breakfast, salty snacks, total snacks and decreased physical activity. A similar association was noted in the present study also. ¹⁵ CONCLUSION: The poor nutrition quality and sedentary lifestyle established during the epidemic may be difficult to reverse for parents and children. Childhood is a crucial time for learning and inculcating healthy eating habits, which will continue into adulthood. In addition, poor nutrition at a young age could have long-term consequences. The immune system and disease predisposition are inextricably connected to nutrition. Notwithstanding the constraints, this study was able to demonstrate a definite correlation between eating habits and health outcomes in children. A long-term follow-up study with a larger sample size will definitely contribute to a better understanding of the nutritional fallouts of the pandemic and help devise suitable mitigation strategies. LIMITATION OF THE STUDY: A limited and consecutive sample that may not completely represent the population. Further, the socio-economic conditions, parental influence on the child&#39;s lifestyle, and diet chart were not a part of the research data. Interpolation of these data may contribute more to a better understanding of the study&#39;s outcome. Funding: No funding sources. Conflict of interest: None declared. &nbsp; <strong>REFERENCES:</strong> &nbsp;Teixeira MT, Vitorino RS, da Silva JH, Raposo LM, Aquino LA, Ribas SA. Eating habits of children and adolescents during the COVID‐19 pandemic: The impact of social isolation. Journal of Human Nutrition and Dietetics. 2021 Aug;34(4):670-8. Deepika, B., Shalini, B., &amp; Monika, A.&nbsp; &quot;The Impact of COVID-19 on Children and Adolescents: Early Evidence in India,&quot; 2021. ORF Issue Brief No. 448,&nbsp; Observer Research Foundation Xiang M, Zhang Z, Kuwahara K. Impact of COVID-19 pandemic on children and adolescents&#39; lifestyle behavior larger than expected. Prog Cardiovasc Dis. 2020;63(4):531-532. doi:10.1016/j.pcad.2020.04.013 Zemrani B, Gehri M, Masserey E, Knob C, Pellaton R. A hidden side of the COVID-19 pandemic in children: the double burden of undernutrition and overnutrition. Int J Equity Health. 2021;20(1):44.&nbsp; Littlejohn P, Finlay BB. When a pandemic and an epidemic collide: COVID-19, gut microbiota, and the double burden of malnutrition. BMC Med. 2021;19(1):31.&nbsp; Jalal SM, Beth MRM, Al-Hassan HJM, Alshealah NMJ. Body Mass Index, Practice of Physical Activity and Lifestyle of Students During COVID-19 Lockdown. J Multidiscip Healthc. 2021;14:1901-1910&nbsp; Azoulay E, Yackobovitch-Gavan M, Yaacov H, et al. Weight Status and Body Composition Dynamics in Children and Adolescents During the COVID-19 Pandemic. Front Pediatr. 2021;9:707773.&nbsp; Wen J, Zhu L, Ji C. Changes in weight and height among Chinese preschool children during COVID-19 school closures. Int J Obes (Lond). 2021;45(10):2269-2273.&nbsp; Jia P, Zhang L, Yu W, et al. Impact of COVID-19 lockdown on activity patterns and weight status among youths in China: the COVID-19 Impact on Lifestyle Change Survey (COINLICS) [published correction appears in Int J Obes (Lond). 2021 Feb 12;:]. Int J Obes (Lond). 2021;45(3):695-699.&nbsp; Stavridou A, Kapsali E, Panagouli E, et al. Obesity in Children and Adolescents during COVID-19 pandemic. Children (Basel). 2021;8(2):135. Published 2021 Feb 12.&nbsp; Perrar I, Alexy U, Jankovic N. Changes in Total Energy, Nutrients and Food Group Intake among Children and Adolescents during the COVID-19 Pandemic-Results of the DONALD Study. Nutrients. 2022;14(2):297.&nbsp; Alghadir AH, Iqbal ZA, A Gabr S. The Relationships of Watching Television, Computer Use, Physical Activity, and Food Preferences to Body Mass Index: Gender and Nativity Differences among Adolescents in Saudi Arabia. Int J Environ Res Public Health. 2021;18(18):9915. Roy S, Tiwari S, Kanchan S, Bajpai P. Impact of COVID-19 pandemic led lockdown on the lifestyle of adolescents and young adults. Indian Journal of Youth and Adolescent Health (E-ISSN: 2349-2880). 2020 Dec 11;7(2):12-5.&nbsp; Shalitin S, Phillip M, Yackobovitch-Gavan M. Changes in body mass index in children and adolescents in Israel during the COVID-19 pandemic [published online ahead of print, 2022 Feb 16]. Int J Obes (Lond). 2022;1-8.&nbsp; Androutsos O, Perperidi M, Georgiou C, Chouliaras G. Lifestyle Changes and Determinants of Children&#39;s and Adolescents&#39; Body Weight Increase during the First COVID-19 Lockdown in Greece: The COV-EAT Study. Nutrients. 2021;13(3):930.&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;

The consecutive k-out-of-m-from-n: F system consists of n components ordered linearly or circularly, it fails if, and only if among any m-consecutive components, there is at least k failed components. In this paper, a new algorithm to find the reliability and the failure functions of the consecutive k-out-of-m-from-n: F linear and circular systems is obtained

Extended-spectrum beta-lactamases (ESBLs), AmpC-type beta-lactamases (ACBLs) and carbapenemases are among the most important resistance mechanisms in Enterobacteriaceae. This study investigated the presence of these resistance mechanisms in consecutive non-replicate isolates of Escherichia coli (n = 2,352), Klebsiella pneumoniae (n = 697), and Proteus mirabilis (n = 275) from an Italian nationwide cross-sectional survey carried out in October 2013. Overall, 15.3% of isolates were non-susceptible to extended-spectrum cephalosporins but susceptible to carbapenems (ESCR-carbaS), while 4.3% were also non-susceptible to carbapenems (ESCR-carbaR). ESCR-carbaS isolates were contributed by all three species, with higher proportions among isolates from inpatients (20.3%) but remarkable proportions also among those from outpatients (11.1%). Most ESCR-carbaS isolates were ESBL-positive (90.5%), and most of them were contributed by E. coli carrying bla CTX-M group 1 genes. Acquired ACBLs were less common and mostly detected in P. mirabilis. ESCR-carbaR isolates were mostly contributed by K. pneumoniae (25.1% and 7.7% among K. pneumoniae isolates from inpatients and outpatients, respectively), with bla KPC as the most common carbapenemase gene. Results showed an increasing trend for both ESBL and carbapenemase producers in comparison with previous Italian surveys, also among outpatients.

Ziziphus Spina Christi was intercropped with barley [Hordeumvulgare] under irrigation regimes in saline soils of dry lands of Sudan. That aimed to find out suitable agroforestry system to suit saline soils as well as to investigate the effect of Z. spinachristspacing on barley yield as a winter fodder crop. The experiment was laid out in terms of a completely randomized block design with 3replicates. Where the trees as the main factor spaced at 4x4mbesides barley crop that inter sown at two levels from the tree truck at 1 m [ZS1] and 1.5 m [ZS2] at two consecutive seasons in 2018 and 2019. Besides soil samples were determined in terms of pH, N, P, K, Organic Carbon at two depths 0-30 cm and 30-60cm. The trees were measured in terms of tree growth namely; tree height, tree collar and canopy diameters, and fruit yield per tree. While barley crop was determined in terms of plant height, a number of plants, and forage yield as fresh and dry per ha per ha as well as a land equivalent ratio. The results revealed that tree growth and fruit yield did not differ in the first season of 2018. Whereas in 2019; tree height was increased by 40 cm and 38 cm when compared ZS1 and ZS2 with control. Similarly, tree collar and canopy diameters were significant under ZS1. Barley biomass dry weight was increased by 78% and 112% when comparing ZS1 with ZS2 and control respectively. Z. spinachristifruit yield was higher under ZS2 than ZS1 and control. Soil K, P, Organic carbon, and C/N were higher under intercropped plots, particularly at 0-30 cm depth. Soil salinity increased by increasing soil depths. Barley plant height was higher under control than intercropped ones in 2018. The land equivalent ratio [LER] was advantageous particularly in 2019, it recorded 10 in ZS2 when compared with ZS1 which recorded 8. Therefore ZS2 is most suitable for intercropping barley with Z.spinachristito to maintain food security and halt desertification in dry lands.

Introduction: Coronary embolism (CE) is recognized as an important non-atherosclerotic cause of acute myocardial infarction (AMI). Atrial fibrillation (AF) is associated with systemic thromboembolism, and the CHADS2 and CHA2DS2-VASc scores are known to be useful for risk stratification. Therefore, we investigated the clinical features and prognosis of CE, and assessed the potential usefulness of these scores for predicting CE. Methods: We studied a total of 2,115 consecutive patients with AMI (M/F 1,528/587, age 68±12 [SD] years) hospitalized between 2001 and 2013. CE was diagnosed according to the criteria shown in Figure 1 Results: The overall prevalence of CE in AMI was 2.4% (n=51, M/F 31/20, age 65±14 years). Compared with non-CE AMI patients, CE patients were characterized as lower prevalence of risk factors. Most common cause of CE was AF (73%). However, only 15 (41%) out of 37 AF patients were treated with vitamin K antagonists (VKAs) and their PT-INR was low, 1.42 (range, 0.95-1.80) at the onset of AMI. Importantly, among 28 CE patients with nonvalvular AF, 17 patients (59%) had a CHADS2 score of 0 or 1. When those particular patients were re-evaluated by CHA2DS2-VASc score, 10 out of 17 (59%) were categorized into a higher risk category (≥ 2) that would benefit from VKAs therapy. During a median follow-up of 4.1 years (interquartile range, 1.5-7.0 years), 8 patients (16%) had major adverse cardiovascular events and 5 patients (10%) recurred CE or systemic embolization (Figure 2). Conclusions: AF is the major underlying cause of CE, recurrence of which seems to be not rare. The CHA2DS2-VASc score may provide reliable risk stratification with a superior ability to predict CE.

Academics clinical education is significant backbone of physiotherapy professionals' schooling and it is express as vital components w h i c h m a k e s r e a d y p r o f e s s i o n a l s o f physiotherapy for experience in clinical set-up.Objective: To investigate understudies' view of how the dual role of CEs as mentor and evaluator affected T-L relationship.Methodology: Self-oriented questionnaire was used using the quantitative research approach. A crosssectional survey design was used in this study. Consenting undergraduate physiotherapy clinical students from university of Lahore, Pakistan who had clinical education for at least one year completed the questionnaire. Consecutive sampling was used to recruit samples of 225 understudies.Results: The difficulties were noticed when CE needed tobehave and acting as the two evaluator and guider to the necessity of understudies. They change their behavior. This affected the relationship of teaching and learning thus affected the studying of undergrad learners. Desires for understudies and CE were frequently not satisfied.Conclusions: Discoveries found out in investigation, based onthe perspectives or the encounters that understudies have of double job of their CEs, become featured. This situation become critical to think about difficulties which are faced by understudies so as to limit possible harmful impacts on understudies' studying environment caused by difficulties

<strong>Potential antidiabetic effect of ethanolic and aqueous-ethanolic extracts of <em>Ricinus communis </em>leaves on streptozotocin-induced diabetes in rats</strong> &nbsp; Mohamed A. M. Gad-Elkareem, Elkhatim H. Abdelgadir, Ossama M. Badawy, Adel Kadri <strong>ABSTRACT</strong> Recently, herbal drugs and their bioactive compounds have gained popularity in the management of diabetes mellitus (DM) which has become an epidemic disease all over the world, especially prevalent in the Kingdom of Saudi Arabia (KSA). This study aimed to investigate the antidiabetic effect of ethanolic and aqueous-ethanolic extracts of wild <em>Ricinus communis</em> (<em>R. communis</em>) leaves in streptozotocin (STZ) induced diabetic rats. Diabetic rats were administered orally with the mentioned extracts at doses of 300 and 600 mg/kg/BW for 14 days, and the obtained results of different biochemical parameters were compared with normal control, diabetic control and standard drug glibenclamide (5 mg/kg/BW). The obtained results revealed a remarkable and significantly (<em>P</em>&lt;0.05) reverse effect of the body weight loss, observed when diabetic rats were treated with ethanol and aqueous-ethanol extracts at 300 mg/kg/BW. Administration of the ethanol extract at 600 mg/kg/BW significantly (<em>P</em>&lt;0.05) reduced the blood glucose level. A significant increase in the AST, ALT and ALP levels (<em>P</em>&lt;0.05) was observed in the diabetic control and in the experimental groups with glibenclamide which was also significantly (<em>P</em>&lt;0.05) lowered after treatment with extracts at special doses. Total proteins, albumin, total bilirubin, direct bilirubin, creatinine and urea were also investigated and compared to the corresponding controls. We showed that administration of <em>R. communis</em> extract generally significantly (<em>P</em>&lt;0.05) ameliorated the biochemical parameters of diabetic rats. Also, the changes in serum electrolyte profile were assessed and the results demonstrate that administration of &nbsp;extracts at concentration of 600 mg/kg/BW generally inhibits the alteration maintain their levels. The obtained data imply the hypoglycemic effects of this plant, which may be used as a good alternative for managing DM and therefore validating its traditional usage in KSA. &nbsp; <strong>Collection of plant materials </strong> The leaves of <em>R. communis </em>were harvested in November 2017 from a mountain in Buljurashi<em> City</em>, Al Baha, Saudi Arabia, with coordinates <em>19&deg;51&prime;34&Prime;N 41&deg;33&prime;26&Prime;E. </em>&nbsp;Voucher specimens with the corresponding number BRC100 were deposited at the Chemistry Department, College of Science and Arts in Baljurashi, Al Baha University. This work was supported by Deanship of Scientific Research, Project number: 71/1438, Albaha University, Kingdom of Saudi Arabia. <strong>Preparation of plant extract </strong> The leaves of <em>R. communis </em>were dried at room temperature, ground into a fine powder and stored at 5&deg;C until needed. 200 g of <em>R. communis</em> powder were added to 500 mL ethanol (96%) and a mixture of aqueous-ethanol (with ratio 60:40). When obtaining the plant extract, we followed the same method as done by<em> Bakari et al. (2015</em><em>)</em>, and then the plant extract was reconstituted with distilled water for oral administration. <strong>Experimental Animals&nbsp; </strong> Forty two Male Wistar rats 12-week-old (150-160g) were obtained from the Animal Care Center, College of Pharmacy, King Saud University, Riyadh, Saudi Arabia. Animals were maintained on a 12 h light/dark in cycle polypropylene cages (six rats in each) at the ambient temperature of 2 3 &plusmn; 2 &deg;C and relative humidity of 50-60% with food and water provided ad libitum. All experiments were carried out according to the recommendation of Experimental Animals Ethics Committee of The King Saud University in accordance with the international standards for the handling of experimental animals. The rats were acclimatized for 1 week before the start of the experiment. &nbsp; <strong>Toxicity profile </strong> In this study, acute toxicity study was carried according to Organization for Economic Cooperation and Development, guideline 423. A limit dose of 2 000 mg/ kg body weight /oral was used. The signs of toxic effects and/or mortality were observed 3 h after administration then for the next 48 h. The body weight was recorded for consecutive 14 days. Since the extracts were found safe up to the dose level of 2000 mg/kg body weight, a dose of 300 and 600 mg/kg body weight of the two extracts was selected for screening of the antidiabetic activity. <strong>Induction of diabetes </strong> Rats were fasted overnight and experimental diabetes was induced by intraperitoneal injection of 55 mg/kg body weight of streptozotocin (STZ, Sigma, St Louis, MO, USA) dissolved in freshly prepared citrate buffer (0.1 mol/L, pH 4.5) (<em>Arora et al., 2010</em>). Fasting blood sugar for the animals was measured after 72 h using Medisafe Mini Blood Glucose Reader (TERUMO Corporation Ltd., Hatagaya, Tokyo, Japan). Rats with fasting blood sugar level more than 200 mg/dL (11.1 mmol/L) were considered as diabetic and used for the study. Rats were then allowed to develop diabetes for 14 days (<em>Arora et al., 2010)</em>. <strong>Experimental design</strong> Oral glucose tolerance test with extracts in diabetic rats: Forty two rats (36 diabetic surviving rats and 6 normal rats) were divided into seven groups of six rats each. The animals were treated orally once daily for 14 consecutive days as follows. - Group 1, normal rats were treated with distilled water and used as the negative control. - Group 2, diabetic control rats were treated with distilled water. - Group 3, diabetic rats were given standard drug glibenclamide (5 mg/kg body weight) (<em>Alamin et al., 2015</em>). - Groups 4 and 5, served as diabetic rats given ethanolic <em>R. communis </em>extracts at doses of 300 mg/ kg and 600 mg/ kg respectively, once daily for 14 days, - Groups 6 and 7, served as diabetic rats given aqueous-ethanol extract at doses of 300 mg/ kg and 600 mg/ kg respectively, once daily for 14 days. Normal control rats and untreated diabetic rats received equal volumes of water in place of the extract. The body weight was measured every day and the dose was calculated accordingly. &nbsp; <strong>Collection of blood samples and estimation of biochemical parameters</strong> Blood samples were collected from overnight fasted rats (only water allowed) after 2 weeks of treatment under diethyl ether anesthesia by cardiac puncture (good quality and large volume of blood from the experimental animals) into heparinized and non-heparinized tubes for hematological and biochemical analyses. &nbsp;For serum samples, blood was allowed to coagulate, followed by centrifugation at 3000 r/min for 15 min at 4 &deg;C to separate serum. Sera were divided into aliquots and stored at -80 &deg;C for biochemical assay. <strong>Biochemical analysis </strong> For biochemical analysis we used standard commercial kits according to the manufacturer<em>&#39;s</em>&nbsp;instructions. Fasting serum glucose level was determined on day 14 by glucose oxidase-peroxidase method using the kit from RANDOX Laboratories Ltd, UK. Alanine and aspartate aminotransferase (ALT and AST) (<em>Schmidt and Schmidt, 1963</em>) and alkaline phosphatase (ALP) (<em>Wright, 1972</em>) were measured using kits from Randox Laboratory Ltd., UK. Serum creatinine (<em>Owen et al., 1954</em>), serum sodium, potassium, chloride, phosphorus and carbon dioxide (<em>Tietz et al., 1994</em>), bilirubin (<em>Malloy and Evelyn, 1937</em>) total protein, albumin (<em>Spencer and Price, 1977</em>) and urea (<em>Marsh et al., 1965</em>) were determined using a commercial kit from QUIMICA Clinica Aplicada, Amposta, Spain. <strong>Statistical analysis</strong> A one-way analysis of variance (ANOVA) and Tukey&#39;s post-hoc test were performed to determine significant differences between the parameters using the SPSS 19 statistical package (SPSS Ltd. Woking, UK). Means and standard errors were calculated. 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In vitro cytotoxicity and antimicrobial properties. <em>Lipids in Health and Disease</em> <strong>11</strong>:102 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>Figure:</strong> The effect of <em>Ricinus communis </em>leaves extracts on the blood glucose in STZ induced diabetic rats after 2 weeks of treatment. &nbsp; STZ: Control diabetic rats; STZ+EE300 mg/kg/BW: STZ + Ethanol extract at 300 mg/kg/BW; STZ+AE-300 mg/kg/BW: STZ + Aqueous-ethanol at 300 mg/kg/BW; STZ+ E600mg/kg/BW: STZ + Ethanol at 600 mg/kg/BW; STZ+AE600 mg/kg/BW: STZ + Aqueous-ethanol at 600 mg/kg/BW &nbsp; *Values are statistically significant at <em>p </em>&lt;0.05 **Values are statistically significant at <em>p </em>&lt;0.01 The data were analysed using the parametric method, ANOVA followed by Tukey&#39;s post-hoc test. &nbsp; &nbsp;

Authors: Sandeep Kumar Vashist, Gregor Czilwik, Thomas van Oordt, Felix von Stetten, Roland Zengerle, E. Marion Schneider &amp; John H.T. Luong ### Abstract A rapid one-step kinetics-based sandwich enzyme-linked immunosorbent (ELISA) procedure has been developed for highly-sensitive detection of C-reactive protein (CRP) in less than 30 min. With minimal process steps, the procedure is highly simplified and cost-effective. The analysis only involves sequentially the formation of a sandwich immune complex on capture anti-CRP antibody (Ab)-bound Dynabeads, followed by two magnet-assisted washings and an enzymatic reaction. The developed immunoassay (IA) detected CRP in the dynamic range of 0.3-81 ng mL-1 with a limit of detection and analytical sensitivity of 0.4 ng mL-1 and 0.7 ng mL-1. Its analytical precision for analysis of CRP spiked in diluted human serum, whole blood, and ethylenediaminetetraacetic acid (EDTA) plasma samples of patients was validated by conventional ELISA, unravelling its immense potential for in vitro diagnostics (IVD). ### Introduction As the gold standard for the detection of CRP in clinical diagnostics, ELISA exhibits high-throughput, excellent reproducibility, high precision and remarkable sensitivity. Last five decades have accumulated over 300,000 peer-reviewed articles related to ELISA. In particular, the last decade has also witnessed considerable advances in diversified CRP assay formats (1-22), lateral flow (20), immunoturbidimetry (1,11), surface plasmon resonance (14), piezoresistive cantilever-based IA (10), chemiluminescent IA (3), impedimetry (23), electrochemistry17, reflectometric interference spectroscopy19, microfluidics (7) and homogenous bead-based IA (24). In general, most of these assay formats are based on a complex procedure comprising of many process steps with a lengthy analysis time (25-28). Therefore, there is uttermost importance for the development of rapid and cost-effective IA procedures with high precision and minimal process steps to guide healthcare professionals to decide on the desired intervention at an early stage. CRP, a pentameric protein with a molecular weight of 118 kDa, is a member of a class of acute-phase reactants indicating activation of innate and adaptive immunity (13,29,30). It plays an important role in host defense by binding to phosphocholine and related microbial molecules. As an early indicator of infectious or inflammatory conditions (31,32), CRP is usually elevated in patients with neonatal sepsis (33-35), meningitis, pancreatitis, pneumonia and pelvic inflammatory disease and occult bacteremia. The significantly elevated serum CRP levels are associated with malignant diseases, bacterial infections and correlate with increased 30-day mortality rates in hospitalized patients (36). The monomeric CRP binds to the surface of damaged cells and platelets, thereby activating the complement cascade that plays an important role in inflammation. The American Heart Association/Center for Disease Control has considered CRP as the best inflammatory marker for clinical diagnosis (37). The precise and rapid determination of human C-reactive protein (CRP) is essential for diagnosis and management of neonatal sepsis (33-35,38,39), cardiovascular diseases (40-44), infectious/inflammatory conditions (31) and diabetes (45-47). The ability for repeated CRP measurements with high precision in an acute setting provides clinicians with the valuable information to assess disease diagnosis and circumvent any unnecessary administration of antibiotics. The normal CRP levels in human serum are usually below 10 µg mL-1 30 but up to 350-400 µg mL-1 in several disease states. The CRP levels in the ranges of 10-40 µg mL-1, 40-200 µg mL-1, and &gt;200 µg mL-1 are the indicators of mild or chronic inflammation and viral infections; acute inflammation and bacterial infections; and severe bacterial infections and burns, respectively (30). The CRP levels beyond the cut-off point of 5 µg mL-1 are indicative of neonatal sepsis, which is diagnosed based on the determination of two CRP concentration ranges normal (0.2-480 µg mL-1) and high sensitivity (0.08-80 µg mL-1)30. The high sensitivity CRP assay is performed first, but the normal CRP assay is also performed if the CRP levels are &gt;80 µg mL-1. The existing analytical techniques for the determination of CRP have limitations in terms of prolonged IA duration and lower analytical sensitivity, as reviewed recently by Algarra et al.(22). The clinical laboratory-based CRP assays, based on latex agglutination or nephelometry, and phosphocholine and O-phosphorylethanolamine based immunoassays can detect CRP only in the detection range of µg mL-1. On the other hand, the recently developed immunoassay formats, based on electrochemical techniques, nanoparticles, nanocomposites, chemiluminescence, total internal reflection and micromosiac immunoassays, have higher sensitivities in the range of ng mL-1 to µg mL-1. Similarly, the surface plasmon resonance based real-time and label-free immunoassay formats have sensitivity between ng mL-1 to g mL-1. Therefore, there is a critical need for a highly simplified, cost-effective, precise and highly sensitive IA format for the rapid detection of CRP. We have developed a rapid one-step kinetics-based sandwich ELISA procedure (48) (Figure 1) to detect CRP in human whole blood and serum in less than 30 min. It has critically reduced the IA duration by more than 12-fold and the analysis cost by 2.5-fold in comparison to the conventional procedure. This novel ELISA format required also significantly reduced number of process steps and only two washing steps in comparison to the conventional counterpart (Table S1). Moreover, the high analytical precision of the developed procedure implies its tremendous potential for rapid analyte detection in clinical and bioanalytical settings. ### Materials 1. Human CRP Duoset kit (R &amp; D Systems, UK, cat. no. DY1707E) ! - CAUTION Store reconstituted Ab and antigen at 2-8 °C, if they are used within a month. Otherwise, make aliquots and store at -20 °C to -70 °C for up to 6 months. The kit comprises of - Mouse anti-human CRP capture Ab (360 μg mL-1) - Recombinant human CRP (90 ng mL-1) - Biotinylated mouse anti-human CRP detection Ab (22.5 µg mL-1) - Streptavidin-conjugated horseradish peroxidase (SA-HRP) - !CAUTION Do not freeze. Store in the dark as streptavidin is light-sensitive. - The Human CRP Duoset kit’s components can also be procured separately, i.e. human CRP antibody (cat. no. MAB17071), human CRP biotinylated antibody (cat. no. BAM17072) and recombinant human CRP (cat. no. 1707-CR). - Blocker BSA in PBS (10X), pH 7.4, 10% (w/v) (Thermo Scientific, Ireland, cat. no. 37525) CRITICAL Filter with 0.2 µm pore size filter paper prior to use to avoid contamination. - Dynabeads® M-280 Tosylactivated (Thermo Fisher Scientific, Ireland) - Sulfuric acid (Aldrich, cat. no. 339741) - !CAUTION Avoid skin contact as it is a strongly corrosive agent and an irritant. Use personal protective equipment (PPE), such as chemical safety glasses, chemical-resistant shoes and lab coats, for handling. Handle only in a fume cabinet. In case of skin contact, wash immediately with acid neutralizers and seek medical advice as soon as possible. - BupH Phosphate Buffered Saline Packs (0.1 M sodium phosphate, 0.15 M sodium chloride, pH 7.2) (Thermo Scientific, Ireland, cat. no. 18372) !CAUTION Avoid inhalation. CRITICAL Prepare in autoclaved DIW (18Ω), see REAGENT SETUP. - TMB substrate kit (Thermo Scientific, Ireland, cat. no. 34021) - TMB solution (0.4 g L-1) - !CAUTION Skin, eye and lung irritant. In case of skin contact, wash with plenty of water. CRITICAL The TMB to peroxide ratio is critical for color development. Maintain the ratio 1:1. - Hydrogen peroxide solution (containing 0.02 % v/v H2O2 in citric acid buffer) (Thermo Scientific, Ireland). - !CAUTION Strong oxidizing agent. Harmful if swallowed. Severe risk of damage to eyes. Rinse immediately with plenty of water in case of contact and seek medical attention. Wear suitable protection and work in a safety cabinet or fume cupboard. - Human whole blood (HQ-Chex level 2, cat. no. 232754, Streck) 180 day closed-vial stability and 30 day open-vial stability. - Human serum (CRP free serum, cat. no. 8CFS, HyTest Ltd., Finland) - Deionized water (18 Ω, DIW). (Direct-Q®3 Water Purification System, Millipore, USA) - Nunc microwell 96-well polystyrene plates, flat bottom (non-treated), sterile (Sigma Aldrich, cat. no. P7491) - Eppendorf microtubes (1.5 mL; Sigma Aldrich, cat. no. Z606340) - Sigmaplot software version 11.2 from Systat REAGENT SETUP 1. PBS. Add a BupH Phosphate Buffered Saline Pack to 100 mL of autoclaved DIW, dissolve well and make the volume up to 500 mL using autoclaved DIW. Each pack makes 500 mL of PBS at pH 7.2, which can be stored at RT for a week and at 4 ºC for up to four weeks. - Binding buffer. 0.1% BSA in PBS, pH 7.2. - Washing buffer. 0.05% Tween® 20 in PBS, pH 7.2. - Anti-CRP capture Ab-bound Dynabeads®. The anti-CRP capture Ab was bound to the tosylated Dynabeads® using the standard immobilization procedure provided by the manufacturer (Invitrogen). The prepared stock solution of anti-CRP capture Ab-bound Dynabeads® was then stored at 4 °C. - Biotinylated anti-CRP detection Ab conjugated to SA-HRP. Biotinylated anti-CRP detection Ab conjugated to SA-HRP was prepared by adding 1 µL of biotinylated anti-CRP detection antibody (0.5 mg mL-1) to 1 µL of SA-HRP to 2998 µL of the binding buffer followed by 20 min of incubation at room temperature (RT). As a result, the concentration of biotinylated anti-CRP detection Ab used was 0.17 µg mL-1, while SA-HRP dilution employed was 1:3000. ### Equipment 1. -70 °C freezer (operating range -60 to -86 °C) (New Brunswick) - 2-8 °C refrigerator (Future, UK) - Direct-Q® 3 water purification system (Millipore, USA) - Tecan Infinite M200 Pro microplate reader (Tecan, Austria GmBH) - Mini incubator (Labnet Inc., UK) - Quadermagnet magnetic holder (Supermagnete, Germany) - PVC fume cupboard Chemflow range (CSC Ltd.) ### Procedure **Preblocking TIMING ~ 30 min** 1. Block the MTP wells by incubating with 300 μL of 5% (w/v) BSA for 30 min a 37 °C and wash with 300 μL of wash buffer five times. Washing can also be performed with an automatic plate washer. The preblocking is essential to prevent non-specific binding of IA reagents to the MTP wells (49). CRITICAL STEP Use filtered BSA or filter the BSA solution prior to use to remove any microbial or other contaminants. ?TROUBLESHOOTING **One-step kinetics-based CRP sandwich ELISA TIMING 30 min** - 2.Dispense in the BSA-blocked MTP wells sequentially 2 µL of the diluted stock solution of anti-CRP capture Ab-bound Dynabeads® (diluted 1:10 in binding buffer), 38 µL of the binding buffer and 40 µL of biotinylated anti-CRP detection Ab (0.17 µg mL-1) pre-conjugated to SA-HRP (diluted 1:3000). Finally, dispense 40 µL of CRP (varying concentrations; 0.3-81 ng mL-1) in the respective MTP wells in triplicate. Place the MTP on the magnetic holder and incubate at 37 °C for 15 min so that the magnets capture the Dynabead®-bound sandwich immune complex. Take out the excess reagents by sucking back the solution using a 300 µL multi-channel pipette. ?TROUBLESHOOTING - 3.Wash the magnetically-captured sandwich immune complex-bound Dynabeads® twice by dispensing and sucking back 300 µL of the washing buffer using a 300 µL multi-channel pipette. Thereafter, suspend the washed magnetically-captured sandwich immune complex-bound Dynabeads® in 50 µL of the binding buffer. - 4.Add 100 µL of the TMB-H2O2 mixture to each MTP well and incubate at RT for 4 min to allow the enzymatic reaction to develop color. ?TROUBLESHOOTING - 5. Stop the enzymatic reaction by adding 50 µL of 2N H2SO4 to each MTP well. - 6. Measure the absorbance at a primary wavelength of 450 nm and 540 nm as the reference wavelength in the Tecan Infinite M200 Pro microplate reader. CRITICAL STEP Determine the absorbance within 10 min of stopping the enzymatic reaction. ### Troubleshooting  ### Anticipated Results The developed CRP sandwich ELISA critically reduced the IA assay duration by 12-fold, from 6 h (commercial CRP sandwich ELISA) to just 30 min, based on the use of Ab-bound Dynabeads®/MTPs. The developed ELISA is cost-effective and highly-simplified as attested by the minimal process steps and 2.5-fold reduced IA components in comparison to the conventional ELISA procedure (Tables S1, S2). It detects 0.3-81.0 ng mL-1 of CRP with linearity in the range of 1-81 ng mL-1 (Figure 2A). LOD, analytical sensitivity and correlation coefficient (R2) are determined to be 0.4 ng mL-1, 0.7 ng mL-1, and 0.998, respectively (Table S2). The intraday and interday variability determined from five assay repeats (in triplicate) in a single day and five consecutive days, respectively, are in the ranges of 0.7-10.8 and 1.6-11.2, respectively. The developed ELISA can detect the entire pathophysiological range of hsCRP from 3-80 µg mL-1 in human whole blood and serum after appropriate dilution, as demonstrated by the detection of CRP spiked in diluted whole blood and plasma (Figure 2A). It has high specificity for CRP, as demonstrated by the use of various experimental process controls (Figure 2B) that shows no detectable interference with the immunological reagents. The optimum duration for the formation of the sandwich immune complex by the one-step kinetics-based procedure is 15 min, while the optimum number of magnet-assisted washings thereafter is only two (Figure S1). The developed and conventional sandwich ELISAs have the same analytical precision for the detection of CRP in diluted whole blood and serum as the results are in agreement with each other (Table 2). The percentage recovery for the CRP-spiked diluted human whole blood is in the range of 93.3-107.0 and 94.0-103.3 for the developed and conventional sandwich ELISAs, respectively. Similarly, the percentage recovery for CRP-spiked diluted human serum ranges from 103.3 -108.0, compared to 93.3-113.0 for the developed and conventional sandwich ELISAs, respectively. The results obtained for the detection of CRP in the EDTA plasma samples of patients by the developed ELISA are also in good agreement with those obtained by the conventional ELISA (Table 3). The anti-CRP capture Ab-bound Dynabeads® can be stored for more than 4 months at 4 ºC without compromising the CRP detection response (Figure 2C). The production variability for the preparation of anti-CRP capture Ab-bound Dynabeads®, using the same lots of Dynabeads® and anti-CRP capture Ab, is less than 3 percent (Figure 2D). Moreover, the developed ELISA using SA-HRP/biotinylated anti-CRP Ab conjugate is similar to the variant of the developed ELISA procedure that employs the two-step binding of biotinylated anti-CRP Ab and SA-HRP (Figure S2A). The one-step kinetics-based sandwich ELISA solution (comprising anti-CRP capture Ab-bound Dynabeads® and biotinylated anti-CRP detection Ab preconjugated to SA-HRP, stored at 4 ºC in BSA-preblocked MTPs) exhibited no noticeable decrease in its functional activity for up to 4 weeks (Figure S2B). Therefore, taking into account the attributes of the developed generic sandwich ELISA procedure, it can be reliably employed in clinical and bioanalytical settings. Moreover, it has immense potential for the development of novel and fully automated rapid IVD kits in combination with lab-on-a-chip technologies, microfluidics, nanotechnology and smart system integration. ### Figures **Figure 1: Schematic of the protocol**  One-step kinetics-based sandwich ELISA procedure for the rapid detection of C-reactive protein (CRP) (48). Reproduced with permission from Elsevier Inc. **Figure 2: Bioanalytical performance of one-step kinetics-based CRP sandwich ELISA (48)**.  (A) Detection of CRP in PBS (10 mM, pH 7.4), diluted human serum and diluted human whole blood. (B) Specific CRP detection with respect to various experimental process controls (anti-CRP1 and anti-CRP2 are capture and detection antibodies (Ab), respectively). (C) Stability of anti-CRP capture Ab-bound Dynabeads® stored at 4 ºC. (D) Production variability for the preparation of anti-CRP capture Ab-bound Dynabeads® from the same lots of Dynabeads® and anti-CRP capture Ab. 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Effect of high-sensitivity C-reactive protein on the development of diabetes as demonstrated by pooled logistic-regression analysis of annual health-screening information from male Japanese workers. *Diabetes Metab*. 39, 27-33 (2013). - Testa, R. et al. C-reactive protein is directly related to plasminogen activator inhibitor type 1 (PAI-1) levels in diabetic subjects with the 4G allele at position -675 of the PAI-1 gene. *Nutr. Metab. Cardiovasc. Dis*. 18, 220-226 (2008). - Vashist, S. K. et al. One-step kinetics-based immunoassay for the highly-sensitive detection of C-reactive protein in less than 30 minutes. *Anal. Biochem*. 456, 32-37 (2014). - Dixit, C. K., Vashist, S. K., MacCraith, B. D. &amp; O’Kennedy, R. Evaluation of apparent non-specific protein loss due to adsorption on sample tube surfaces and/or altered immunogenicity. *Analyst* 136, 1406-1411 (2011). ### Acknowledgements We thank Dr. Eberhard Barth for providing and anonymizing the leftover EDTA plasma samples of patients treated by intensive care at University Hospital Ulm, Germany for the validation of the developed sandwich ELISA. One-step kinetics-based immunoassay for the highly sensitive detection of C-reactive protein in less than 30min ### Associated Publications Sandeep Kumar Vashist, Gregor Czilwik, Thomas van Oordt, Felix von Stetten, Roland Zengerle, E. Marion Schneider, and John H.T. Luong, *Analytical Biochemistry* 456, 32 - 37 *Source: [Protocol Exchange](http://www.nature.com/protocolexchange/protocols/3197). Originally published online 27 May 2014*.

Original Research Paper <strong>Parental Karyotyping in Recurrent pregnancy loss in tertiary care hospital</strong> <strong>Authors: </strong> <strong>Dr. M. Pravallika, ²Dr. N. Chandraprabha, ³Dr. M.Swarnalatha,⁴Dr. R. Sujatha</strong> <em>Andhra medical College Visakhapatnam</em> <em>Rangaraya medical College Kakinada</em> <em>Andhra Medical College Visakhapatnam</em> <em>Rangaraya medical College Kakinada</em> Corresponding Author: Dr. R. Sujatha, Rangaraya medical College Kakinada <strong>Article Received:</strong>&nbsp; 10-08-2022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <strong>Revised:</strong>&nbsp; 31-08-2022&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <strong>Accepted:</strong> 21-09-2022 <strong>ABSTRACT:</strong> <strong>Introduction:</strong> Recurrent pregnancy loss is a devastating outcome for patients and their clinicians and it continues to be clinical dilemma. <strong>Aims and objectives: </strong>To know the role of chromosomal abnormalities and cytogenetic evaluation in the couples with RPL and to determine the prevalence and types of chromosomal anomalies in couples with RPL. Materials and methods: The couples with recurrent first trimester abortions visiting the Department of OBG King George Hospital, Vishakhapatnam. It is Hospital based observational study for one year from December 2020 to November 2021. In this study detailed clinical evaluation, laboratory investigations and cytogenetic analysis were done. Inclusion criteria: Couples with prior history of two or more abortions and age between 18 -35 years. Exclusion criteria Couples with recurrent second and third trimester loses, congenital female genital tract abnormalities and couples who have not given consent. <strong>Methodology: </strong>At enrollment, after informed consent is taken, information on demographic characteristics, any medical history , family history and clinical data are collected along with a three generation pedigree and recorded as per proforma .All couples are subjected to basic laboratory investigations.After basic clinical and laboratory work up , couples are subjected to cytogenetic analysis.A Peripheral blood sample of about 3 ml is collected and lymphocytes are cultured in presence of a mitogen.After an optimum time of culture mitotic inhibitor colchicine is added to the culture and mitosis is arrested in metaphase as colchicine block the formation of spindle fibres. Peripheral blood lymphocyte cultures are set up according to modified method of Moorhead et al for detection of karyotyping abnormalities using G banding. <strong>Results:</strong> Primary RPL is more common than secondary RPL. The majority belonging to age group 21 to 25 and the majority of males belonging to the age group of 26 to 30 yrs. 42.9% of the couples had a total of 3 abortions. Most common chromosomal anomaly detected were Balanced reciprocal translocations detected in 3 cases(42.8%) and 2 were in females and 1 was in male .Robertsonian translocations were detected in 2 cases(28.57%) , one in male and one in female. Chromosomal inversion was detected in one female (14.2%) and Mosaicism was in 1 female (14.2%). <strong>Conclusion:</strong> Recurrent pregnancy loss is a challenging problem for Obstetricians. Cytogenetic analysis is an essential investigation for couples, in whom genetic counseling and proper management can be planned accurately. <strong><em>Key words: recurrent pregnancy loss, cytogenic, karyotype</em></strong> &nbsp; &nbsp; <strong>INTRODUCTION</strong><strong>:</strong> Recurrent pregnancy loss is a devastating outcome for patients and their clinicians and it continues to be clinical dilemma. According to ACOG early pregnancy recurrent pregnancy loss (RPL) is a distinct disorder defined by two or more pregnancy losses confirmed by ultrasound or histopathology of products of conception.[1]. According to RCOG, Recurrent miscarriage is defined as the loss of three or more consecutive pregnancies, affects 1% of couples trying to conceive. It has been estimated that 1&ndash;2% of second-trimester pregnancies miscarry before 24 weeks of gestation.[2] The European Society for Human Reproduction and Embryology(ESHRE) special interest group for early pregnancy defines recurrent miscarriage as three early consecutive losses or two late pregnancy losses.[3] The current definition does not include women with ectopic, biochemical pregnancies and pregnancy of uncertain location .Each of these conditions is known to be associated with poor obstetric outcome and can be recurrent. The chromosomal abnormalities can be divided in two basic groups: numerical and structural abnormalities. These abnormalities can involve one or more autosomal chromosomes, sexual chromosomes and both simultaneously [3]. They are most commonly found as balanced rearrangements, i.e. abnormalities cause no clinical symptoms in carriers but possibly induce the production of abnormal reproductive cells containing abnormal amounts of genetic material[2]. Apart from the genetic reasons many other reasons contribute to the recurrent abortions and these include the uterine anatomical factors, hormonal factors, immunological and non-immunological mechanisms. Even environmental factors, stress and occupational factors do seem to be related in few cases though there is no strong evidence .Apart from these known etiologies, recurrent pregnancy losses were found to be due to unknown reasons in majority of the patient The risk of miscarriage increases with increasing maternal age and the subsequent pregnancies and the loss of a pregnancy at any stage is a devastating experience to the woman as the chances of a next successful pregnancy outcome decrease. Hence early diagnosis and treatment should be initiated to provide a healthy baby to the mother. <strong>Primary vs Secondary RPL:</strong> Primary recurrent miscarriage: It is defined as two or more losses with no pregnancy progressing beyond 20 weeks. <strong>Secondary recurrent miscarriages</strong>: It is defined as two or more losses after a pregnancy that has progressed beyond 20 weeks which might have resulted in a live or still birth. <strong>Epidemiology </strong> Based on the incidence of spontaneous pregnancy loss , the incidence of recurrent pregnancy loss is approximately 1 in 300 pregnancies[6] .However epidemiological studies have revealed that about 1 -5 % of couples attempting childbirth. Although a clear data is not published , the best available data suggest that risk of miscarriage in subsequent pregnancy after 2 losses is 30 % compared with 33 % after 3 loses. Among the patients without a history of live birth .Hence , it strongly suggests a role of evaluation after just 2 miscarriages in patients with no prior live births .Chromosomal anomalies of parents with recurrent pregnancy losses are observed in about 2 % to 8% of the couples. <strong>Indian scenario:</strong> Among the studies done in India, the prevalence of chromosomal abnormalities varied between 7 and 18%.(8)Genetic causes Approximately 2 to 4% of RPL is associated with a parental chromosomal abnormalitie They include: balanced structural chromosomal rearrangement. Most commonly balanced reciprocal or robertsonian translocations. 2) Chromosomal inversions 3) Mosaicisms.4) Inversions. Types of inversions 1.Peri-centric 2.Para-centric 5)Mendelian disorders.6)Sex chromosome aneuploidies.7) Single nucleotide variants 8) Epigenetic aberrations Under current recommendations, the clinical management of RPL couples includes parental karyotyping as first line genetic test. Karyotyping of both the parents is included in a standard clinical evaluation of the couples with recurrent pregnancy loss. According to Christiansen et al. there is two- to sevenfold increased prevalence of recurrent miscarriages among first-degree relatives compared to the background population[5], and further studies showed that overall frequency of miscarriage among the siblings of patients with idiopathic RPL is approximately doubled compared to that in the general population[6]. Consanguineous marriages also significantly increase the incidence of inherited recessive disorders and cause some reproductive and developmental health problems and also promote recurrent loss of pregnancies. Genetic and genomic studies of RPL potentially have the benefit of understanding the mechanism underlying the cause of RPL, producing a risk estimation for the couple in the future and may suggest a treatment. <strong>AIMS AND OBJECTIVES</strong><strong>:</strong> To know the role of chromosomal abnormalities and cytogenetic evaluation in the couples with Recurrent pregnancy loses. 2) To determine the prevalence and types of chromosomal anomalies in couples with recurrent miscarriages. <strong>MATERIAL AND METHODS:</strong> Study population: The couples with recurrent first trimester abortions visiting the Department of Obstetrics and Gynaecology of King George Hospital , Vishakhapatnam. This study is Hospital based observational study done for one year December 2020 to November 2021. The study was done in 2 parts. In first 10 months Couples were recruited from OBG department and a detailed clinical evaluation, laboratory investigations and cytogenetic analysis were done .in last two months Data analysis was done. Sample size: 70 <strong>Inclusion criteria: </strong> 1. Couples with prior history of two or more abortions. 2. Aged between18 -35 years, after obtaining informed consent. <strong>Exclusion criteria:</strong> 1.Couples with recurrent second and third trimester loses 2.Congenital female genital tract abnormalities. 3.Couples who have not given consent. <strong>METHODOLOGY</strong><strong>:</strong> At enrollment, after informed consent is taken, information on demographic characteristics, any medical history , family history and clinical data are collected along with a three generation pedigree and recorded as per proforma .All the couples are then subjected to basic laboratory investigations , which includes a Complete blood picture , HIV , HbSAg, VDRL , HCV , Blood grouping and typing , Thyroid profile , Fasting and Post prandial blood sugars ,Bleeding and Clotting time. Apart from the routine investigations Semen analysis is done in male partners and Ultrasonography of the pelvis , TORCH and APLA profile are done in the female partners .After basic clinical and laboratory work up , couples are subjected to cytogenetic analysis .in this Peripheral blood sample of about 3 ml is collected and lymphocytes are cultured in the presence of a mitogen.After an optimum time of culture (i.e. 72 hrs for adult sample) , mitotic inhibitor colchicine is added to the culture and mitosis is arrested in metaphase as colchicine block the formation of spindle fibres.Peripheral blood lymphocyte cultures are set up according to modified method of Moorhead et al (1960) for detection of karyotyping abnormalities using G banding.G banding is carried out by modified method of Seabright (1971) A total of 25 intact spread metaphases are screened for each individual with microscope and metaphases will be karyotyped using Cyto vision software.International system for human chromosome nomenclature (ISCN 2016) is followed for the analysis and reporting of the karyotype.Data analysis: Case report forms (Data sheets ) will be used for data collection and it will be tabulated in Microsoft excel. Data analysis will be done using SPS<strong>.</strong> &nbsp; <strong>RESULTS:</strong> Table 1.Types of RPLS with respect to female age groups &nbsp; &nbsp; AGE GROUP &nbsp; Total 18-20 21-25 26-30 31-35 &nbsp; Primary VS secondary &nbsp; Primary Count 3 28 23 4 58 % 100.0% 90.3% 74.2% 80.0% 82.9% &nbsp; Secondary Count 0 3 8 1 12 % 0.0% 9.7% 25.8% 20.0% 17.1% &nbsp; Total Count 3 31 31 5 70 % 100.0% 100.0% 100.0% 100.0% 100.0% &nbsp; CHI SQUARE = 3.504, P VALUE = 0.32 &nbsp; &nbsp; In the present study, majority of the couples ( n=58 , 82.8%) had a non consanguineous marriage .It was followed by third degree consanguineous marriage (n=8 , 11.5%) and second degree consanguineous marriage ( n=4, 5.7%). &nbsp; &nbsp; <strong>figure 2: Pie diagram showing the distribution based on degree of consanguinity</strong> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>Table 2: Types of recurrent pregnancy loss</strong> &nbsp; &nbsp; &nbsp; <strong>Frequency</strong> <strong>Percent</strong> Primary &nbsp;58 82.9 Secondary &nbsp;12 17.1 Total &nbsp;70 100.0 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>Table 3: No of Abortions</strong> &nbsp; <strong>No. of abortions</strong> <strong>Frequency</strong> <strong>Percent</strong> 2 21 30.0 3 30 42.9 4 13 18.6 5 6 8.6 <strong>Total</strong> <strong>70</strong> <strong>100.0</strong> &nbsp; <strong>Table 4 : Types of Chromosomal Anamalies</strong> &nbsp; &nbsp; <strong>FEMALE</strong> <strong>MALE</strong> BALANCED RECIPROCAL TRANSLOCATION 2 1 BALANCED ROBERTSONIAN 1 1 INVERSION 1 0 NUMERICAL ABNORMALITIES 1 0 TOTAL 5 2 Balanced reciprocal translocations are the most common chromosomal aberration recorded in the &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Present study ( n=3 ,42.4%). 2 were observed in females and 1 was in male partner. It was followed by balanced robertsonian translocation, which are observed in 2 cases (n=2,28.5%).1 was observed in female partner and 1 in male partner. Inversion and numerical mosaicism were observed in one case each(14.2% +14.2%), both of them are female carriers. Female to male carrier ratio in our study is 2.5 :1 &nbsp; &nbsp; Table 5. Abnormal Karyotype With Respect to &nbsp;Age and Sex &nbsp; Case Type of chromosomal Anomaly Karyotype Age Sex No of abortions 1 Balanced reciprocal Translocation 46,XX, t(3;6),(q29;q14) 22yrs Female 3 2 Balanced reciprocal Translocation 46,XY,t(6;11),(q14,p15) 28yrs Male 3 3 Balanced reciprocal Translocation 46,XX,t(4:6)(q35;q22) 24 yrs Female 2 4 Robertsonian Translocation 45,XX,rob(13;22) (q10;q10) 26yrs Female 4 5 Robertsonian Translocation 45,XY,rob(14;22) (q10,q10) 29yrs Male 4 6 Inversion 46,XX,inv(9),(p12q21) 24 yrs Female 3 7 Numerical mosaicism mos46XX[22]/45X[3] 32yrs Female 3 &nbsp; <strong>Female</strong> <strong>Male</strong> Hypothyroid 5 2 Hyperthyroid 3 2 Diabetes 3 3 Tuberculosis 1 2 Hiv 1 1 bronchial asthma 1 2 anemia (sickle cell trait) 1 0 heart disease 1 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Table 6: Associated Medical Condition With Respect to Sex. &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>46,XX,t(3;6),(q29;q14).</strong><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 46,XY,T(6;11),(Q14,P15)</strong> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <strong>46,XX,t(4;6)(q35;q22).</strong><strong> 45,XX,rob(13;22),(q10,q10)</strong> &nbsp; &nbsp; 45,XY,ROB(14;22)(Q10;Q10) &nbsp; <strong>46,XX,inv(9),(p12q21)</strong><strong>&nbsp;mos46XX[22]/45X[3]</strong> &nbsp; <strong>DISCUSSSION:</strong> Incidence of RPL is variable all around the world, and is dependent on various factors. Various studies regarding the associated the association of genetic component have been done. <strong>AGE DISTRIBUTION:</strong> In the present study, mean age of the female partners is 25.9 yrs . Majority of the cases in the study belonged to the age group 21 -25 yrs &amp; 26-30 yrs .Mean age of the male partners in the study is 28.87 yrs with majority of the cases between the ages 26 and 30 yrs. <strong>Table-8 Comparison of Mean Ages of Males and Females in Various Studies</strong> <strong>Study</strong> <strong>Female mean age</strong> <strong>Male mean age</strong> Present study 25.9yrs 28.87 yrs Neha Sudhir et al 27.9yrs 32.4 yrs Rim Frikha et al 28 yrs 33 yrs Wiem Ayed et al 31.9yrs 36.6yrs Reza Alibakshi et al 29.33 yrs 33.74yrs Vishali Kalotra et al 31.1 yrs 33.9 yrs &nbsp; <strong>Gender Distribution of Abnormal Karyotype </strong> In the present study, out of the 7 cases with abnormal karyotype 5 were detected in females and 2 were detected in males. female predominance is observed with male to female ratio being 1:2.5. &nbsp; Table -9 Comparison of Male to Female Carrier Ratio <strong>Study</strong> <strong>Male carriers</strong> <strong>Female</strong> <strong>carriers</strong> <strong>Ratio</strong> Present study 2 5 1 : 2.5 Frenny J Sheth et al 49 121 1 :2.1 Vishali Kalotra et al 7 10 1: 1.43 Mau et al 18 9 2:1 Pritti K Priya 3 2 1.5:1 Comparison of chromosomal anomalies in our study to previous studies: In the present study <strong>TYPE OF ABERRATION</strong> <strong>CASES</strong> <strong>%</strong> Balanced reciprocal translocations 3 42.8% Robertsonian translocation 2 28.57% Inversion 1 14.2% Mosaicism 1 14.2% &nbsp; In the present study the incidence of chromosomal anomalies is 10 % of the couples who were showing Recurrent preganacy loss and 5% of the individuals of the affected couples. <strong>Chromosomal anomalies in various studies:</strong> Ashoke K paul etal7 (2018) Total no of couples taken in study were 172. Out of which 17 were found to have chromosomal anomalies. &nbsp; Balanced reciprocal 8 47% Robertsonian 2 11.7% Inversion 5 29.4% Aneuploidy 1 5.8% Mosaic 1 5.8% Zouhair Elkarhat et al [51](2019) Total no. of couples taken in the study were 627. Karyotype analysis showed abnormalities in 69 %. &nbsp; Inversion 27 39.1% Reciprocal translocation 17 24.6% Robertsonian translocation 9 13% Aneuploidy 1 1.4% Mosaicism 4 5.7% Polymorphic variants 8 11.5% Miscellaneous 3 4.3% &nbsp; &nbsp; <strong>IN THE PRESENT STUDY:</strong> In our study 7 individuals had a chromosomal abnormality , out of which 3 (42.8%) were carriers of balanced reciprocal translocation , 2 (28.5%) were carriers of Robertsonian translocations , 1(14.2%) was a carrier of inversion and 1 (14.2%) was a numerical mosaic . These results are comparable to Asoke K Pal et al[7] , in which 4.94 % of the individuals and 88% of the couples with RPL had chromosomal anomalies. Several studies reported different types of structural and numerical chromosomal anomalies in RPL and the percentage of affected couples varied from 4 to 9% . &nbsp; &nbsp; <strong>Table-17: Comparison of Incidence of Chromosomal Anomalies in Different Studies on Recurrent Pregnancy Loss. </strong> <strong>Study</strong> <strong>No. of couples</strong> <strong>Affected</strong> <strong>couples</strong> <strong>%</strong> Present study 70 7 10% Asoke K pal et al(2017) 172 17 9.88% Tusi et al 512 51 9.96% Nazmy et al (2008) 376 34 9.04% Pal et al (2009) 56 5 8.92% Gonclaves et al (2014) 151 11 7.28% &nbsp; &nbsp; <strong>Balanced reciprocal translocations</strong> They are the most common structural chromosomal aberrations associated with recurrent loss of pregnancy in many studies.in the Present Study, balanced reciprocal translocations were recorded in 3 cases, accounting for 42.8% of the total chromosomal anomalies .It is comparable to the above mentioned studies <strong>Robertsonian translocations</strong> Some studies show a higher frequency of Robertsonian translocations. In the study conducted by Pal S et al[12] , Robertsonian translocations were observed in 20% of the cases with chromosoamal anomalies .In the study conducted by Ashalatha et al [13] Robertsonian translocations were observed in 27.27% of the cases with chromosomal anomalies. They are comparable to the present study. In the present study, Robertsonian translocation was identifies in two case out of the seven cases with chromosomal anomalies. It accounts for 28.57% of the cases with chromosomal anomalies,1.4% of the individuals and 2.8% of the couples with recurrent pregnancy loss. <strong>INVERSIONS:</strong> In the present study, chromosomal inversions were observed in 1 cases out of the 7 cases with chromosomal anomalies , accounting for 14.2% . Among the couples with RPL , they account for 1.4% and among the individuals they account for 0.7% . They are second most common anomalies observed after balanced reciprocal translocations. The results in our study are comparable to the study conducted by Wiem Ayed et al [9] . <strong>MOSAICISM:</strong> In the present study , one case was observed out of 7 cases with chromosomal anomalies accounting for 14.2%.Out of the 70 couples taken into the study .Mosaicism accounts for1.4% , and 0.71% of the individuals of the study. The present study is comparable to study done by Rim Frikha et al[10] in 2020 . In it Mosaicism was observed in 2 cases out of 12 cases with chromosomal anomalies accounting it for 16.6%. In the study done by Khalid A Awatarni [11], 14 cases of mosaicism were detected which accounts for 18.18% . The results of the study are comparable to the present study. <strong>LIMITATIONS</strong> The sample size was small. As the present study was a hospital based study , and the patients attending the OPD do not represent a random sample of the population ,the study sample cannot represent whole population <strong>SUMMARY:</strong> A hospital based observational study of Parental karyotyping in recurrent pregnancy loss was undertaken during the period of December 2020 to November 2021 , at the Department of Obstetrics and Gynaecology ,Andhra Medical College , Visakhapatnam. The objectives of the study are : 1).To determine the prevalence of chromosomal anomalies in couples with RPL 2) To know the cause of the RPL and plan for further management like Genetic counseling , ART, PGD etc. With due consideration to the inclusion and exclusion criteria, 70 couples with history of 2 or more pregnancy losses have been recruited in the study . Primary RPL is more common compared to secondary RPL.The mean age of females in the study was 25.59 yrs with majority belonging to age group 21 to 25 and 26 to 30 yrs. The mean of males in the study was 28.87 yrs with majority belonging to the age group of 26 to 30 yrs. Majority of the couples had a total of 3 abortions accounting upto 42.9% of the couples in the study. Most common chromosomal anomaly detected were Balanced reciprocal translocations , which were detected in 3 cases(42.8%) . 2 were females and 1 was detected in male . 1) 46,XX, t(3;6),(q29;q14) 2) 46,XY,t(6;11),(q14,p15) 3) 45,XX,t(4;6)(q35;q22) Robertsonian translocations were detected in 2 cases(28.57%) , one was detected in female and one was detected in male .1) 45,XX,rob(13;12)(q10;q10) 2) 45,XY,rob(4;22)(q10,q10) Chromosomal inversion was detected in one female (14.2%). 46,XX,inv(9),(p12q21) Mosaicism was detected in 1 female (14.2%). 46,XX[22]/45,X[3]. <strong>CONCLUSION:</strong> In the present study, Cytogenetic analysis was done in 70 couples with recurrent pregnancy loss. Abnormal karyotype was observed in 7 cases out of 140 individuals who underwent karyotyping. Translocations are the predominant chromosomal anomalies detected in our present study, followed by Chromosomal inversions and mosaicism. Among the Translocations , Balanced reciprocal were predominant than Robertsonian translocation. Recurrent pregnancy loss is a challenging problem for Obstetricians .Cytogenetic analysis is an essential investigation for couples , in whom genetic counseling and proper management can be planned accurately. Determining the presence of such a rearrangement in a parent is useful because it provides : a)An explanation for the miscarriages b) Information about the risk for a live &ndash;born child with potentially serious anomalies, as well as the risk for future miscarriages c) Availability of prenatal diagnosis in a future pregnancy D) Information for members of extended family who may be at risk and may wish to undergo chromosome testing In those cases with abnormal karyotype in one of the partner, the &ldquo;healthy couple may produce unbalanced gametes resulting in abnormal embryos leading to an abortion. Also embryos with aneuploidies. In these cases ,for further pregnancies pre implantation genetic testing (PGT) can be performed after IVF with trophectoderm biopsy at blastocyst stage to test chromosome content of embryos before replacing back them in uterus. With this approach , the risk of further miscarriage and unbalanced offspring decrease to a percentage similar to that of general population. Some patients with apparently normal karyotypes may require molecular studies for assessment of recurrent risk of miscarriages due to genetic anomalies. Despite the absence of any obvious reasons for RPL, the overall chance of pregnancy is good ( &gt;50%). No intervention is required in most of the couples. <strong>REFERENCES: </strong> 1. Practice Committee of the American Society of Reproductive Medicine.Evaluation and treatment of Recurrent pregnancy loss:Acommitteeopinion.Fertil Steril.2012;98:1103-11. 2. The Investigation and treatment of couples with recurrent pregnancy miscarriages Royal college of Obstetricians and Gynaecologists green top guideline No 17 May2011 [online].Available from :www.rcog.org.uk.[Accessed January,2018]. 3. FarquharsonRG,JauniauxE,Exalto N. Updated and revised nomenclature for description of early pregnancy events. Hum Reprod.2005;20:3008-11. 4. Ford HB, Schust DJ. Recurrent pregnancy loss: etiology, diagnosis, and therapy. Rev Obstet Gynecol. 2009;2(2):76-83. 5. Branch DW, Gibson M, Silver RM. Clinical practice. Recurrent miscarriage. N Engl J Med. 2010;363[18]:1740-7. 6. Management of Recurrent Early Pregnancy Loss. Washington, DC: The American College of Obstetricians and Gynecologists; 2001. The American College of Obstetricians and Gynecologists. (ACOG Practice Bulletin No. 24) 7. l, A. K., Ambulkar, P. S., Waghmare, J. E., Wankhede, V., Shende, M. R., &amp;Tarnekar, A. M. (2018). Chromosomal Aberrations in Couples with Pregnancy Loss: A Retrospective Study. Journal of human reproductive sciences, 11(3), 247&ndash; 253.https://doi.org/10.4103/jhrs.JHRS_124_17. 8. Sheth FJ, Liehr T, Kumari P, Akinde R, Sheth HJ, Sheth JJ. Chromosomal abnormalities in couples with repeated fetal loss: An Indian retrospective study. Indian J Hum Genet. 2013;19(4):415-422. doi:10.4103/0971-6866.124369 9. Ayed W, Messaoudi I, Belghith Z, et al. Chromosomal abnormalities in 163 Tunisian couples with recurrent miscarriages. Pan Afr Med J. 2017;28:99. Published 2017 Sep 29. doi:10.11604/pamj.2017.28.99.11879. 10. Frikha R, Turki F, Abdelmoula N, Rebai T. Cytogenetic Screening in Couples with Recurrent Pregnancy Loss: A Single-Center Study and Review of Literature. J Hum Reprod Sci. 2021;14(2):191-195. doi:10.4103/jhrs.JHRS_74_19. 11 .Awartani KA, Al Shabibi MS. Description of cytogenetic abnormalities and the pregnancy outcomes of couples with recurrent pregnancy loss in a tertiary-care center in Saudi Arabia. Saudi Med J. 2018;39(3):239-242. doi:10.15537/smj.2018.3.21592. 12.Pal S, Ma SO, Norhasimah M, Suhaida MA, Siti Mariam I, Ankathil R, Zilfalil BA. Chromosomal abnormalities and reproductive outcome in Malaysian couples with miscarriages. Singapore medical journal. 2009 Oct 1;50(10):1008. 13. P R A, M M, Shyja. Recurrent pregnancy loss &ndash; Chromosomal anomalies in couples.Int Jour of Biomed Res [Internet]. 2021 Feb. 28 [cited 2021 Dec. 25];12(2):e5576. Available from: https://ssjournals.com/index.php/ijbr/article/view/5576 14.Ikuma S, Sato T, Sugiura-Ogasawara M, Nagayoshi M, Tanaka A, Takeda S. Preimplantation Genetic Diagnosis and Natural Conception: A Comparison of Live Birth Rates in Patients with Recurrent Pregnancy Loss Associated with Translocation. PLoS One 2015;10: e0129958. 15. Dong Y, Li LL, Wang RX, Yu XW, Yun X, Liu RZ. Reproductive outcomes in recurrent pregnancy loss associated with a parental carrier of chromosome abnormalities or polymorphisms. Genet Mol Res 2014;13: 2849-2856. &nbsp; &nbsp;

Elevated Plasma Neurofilament Light and Glial Fbrillary Acidic Protein in Epilepsy Versus Nonepileptic Seizures and Nonepileptic Disorders. Dobson H, Al Maawali S, Malpas C, Santillo AF, Kang M, Todaro M, Watson R, Yassi N, Blennow K, Zetterberg H, Foster E, Neal A, Velakoulis D, O'Brien TJ, Eratne D, Kwan P. Epilepsia. 2024 Sep;65(9):2751-2763. doi: 10.1111/epi.18065 . Epub 2024 Jul 20. PMID: 39032019. Objective: Research suggests that recurrent seizures may lead to neuronal injury. Neurofilament light chain protein (NfL) and glial fibrillary acidic protein (GFAP) levels increase in cerebrospinal fluid and blood in response to neuroaxonal damage, and they have been hypothesized as potential biomarkers for epilepsy. We examined plasma NfL and GFAP levels and their diagnostic utility in differentiating patients with epilepsy from those with psychogenic nonepileptic seizures (PNES) and other nonepileptic disorders. Methods: We recruited consecutive adults admitted for video-electroencephalographic monitoring and formal neuropsychiatric assessment. NfL and GFAP levels were quantified and compared between different patient groups and an age-matched reference cohort (n = 1926) and correlated with clinical variables in patients with epilepsy. Results: A total of 138 patients were included, of whom 104 were diagnosed with epilepsy, 22 with PNES, and 12 with other conditions. Plasma NfL and GFAP levels were elevated in patients with epilepsy compared to PNES, adjusted for age and sex (NfL p = .04, GFAP p = .04). A high proportion of patients with epilepsy (20%) had NfL levels above the 95th age-matched percentile compared to the reference cohort (5%). NfL levels above the 95th percentile of the reference cohort had a 95% positive predictive value for epilepsy. Patients with epilepsy who had NfL levels above the 95th percentile were younger than those with lower levels (37.5 vs 43.8 years, p = .03). Significance: An elevated NfL or GFAP level in an individual patient may support an underlying epilepsy diagnosis, particularly in younger adults, and cautions against a diagnosis of PNES alone. Further examination of the association between NfL and GFAP levels and specific epilepsy subtypes or seizure characteristics may provide valuable insights into disease heterogeneity and contribute to the refinement of diagnosis, understanding pathophysiological mechanisms, and formulating treatment approaches.

&ldquo;#187 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Spin On Super Spacy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33028.40321). @ResearchGate: https://www.researchgate.net/publication/369118224 @Scribd: https://www.scribd.com/document/630547839 @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Spin On Super Spacy } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperSpace). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Space pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; Neutrosophic re-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; Neutrosophic rv-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. ((Neutrosophic) SuperHyperSpace). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme SuperHyperSpace SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme V-SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperSpace &nbsp;and Neutrosophic SuperHyperSpace. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperSpace is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperSpace is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperSpace . Since there&#39;s more ways to get type-results to make a SuperHyperSpace &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperSpace . It&#39;s redefined a Neutrosophic SuperHyperSpace &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperSpace . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperSpace until the SuperHyperSpace, then it&#39;s officially called a ``SuperHyperSpace&#39;&#39; but otherwise, it isn&#39;t a SuperHyperSpace . There are some instances about the clarifications for the main definition titled a ``SuperHyperSpace &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperSpace . For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperSpace&#39;&#39; and a ``Neutrosophic SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperSpace &nbsp;are redefined to a ``Neutrosophic SuperHyperSpace&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperSpace &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperSpace&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperSpace&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperSpace &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperSpace .] SuperHyperSpace . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperSpace if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperSpace &nbsp;or the strongest SuperHyperSpace &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperSpace, called SuperHyperSpace, and the strongest SuperHyperSpace, called Neutrosophic SuperHyperSpace, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperSpace theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperSpace, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperSpace or the Neutrosophic&nbsp;&nbsp; SuperHyperSpace in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperSpace&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperSpace and Neutrosophic&nbsp;&nbsp; SuperHyperSpace, are figured out in sections ``&nbsp; SuperHyperSpace&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39;. In the sense of tackling on getting results and in Space to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperSpace&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperSpace&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperSpace. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperSpace more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperSpace&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperSpace. It&#39;s redefined a \textbf{Neutrosophic SuperHyperSpace} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperSpace But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any k-function space like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function space like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $m$ and $n$ propose special space. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability space $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability space $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be a Neutrosophic Variable in a probability space (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_3,V_4,H\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{12},E_{13}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =4z. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^3. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}= z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; =4z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=6z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=12z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =11z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_j\}_{V^{EXTERNAL}_i\in E_1,V^{EXTERNAL}_j\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^0. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E^{*}_i,E_1,E_3\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z^{|E^{*}_{NSHG}|+2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; = \{V^{EXTERNAL}_1,V^{EXTERNAL}_3,CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=||E_{NSHG}|z^3. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s at least one SuperHyperSpace. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperSpace could be applied. The unique embedded SuperHyperSpace proposes some longest SuperHyperSpace excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperSpace,&nbsp; Neutrosophic SuperHyperSpace, and the Neutrosophic SuperHyperSpace, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperSpace is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperSpace. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperSpace=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperSpace of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperSpace \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperSpace.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperSpace and SuperHyperSpace coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperSpace if and only if it&#39;s a SuperHyperSpace. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperSpace if and only if it&#39;s a longest SuperHyperSpace. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperSpace or the Neutrosophic&nbsp;&nbsp; SuperHyperSpace in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperSpace} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperSpace} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperSpace, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperSpace. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperSpace, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperSpace, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperSpace}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperSpace}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

Photo by Ishan @seefromthesky on Unsplash ABSTRACT A strike to highlight the plight facing contract doctors which has been proposed has received mixed reactions from those within the profession and the public. This unprecedented nationwide proposal has the potential to cause real-world effects, posing an ethical dilemma. Although strikes are common, especially in high-income countries, these industrial actions by doctors in Malaysia are almost unheard of. Reviewing available evidence from various perspectives is therefore imperative to update the profession and the complexity of invoking this important human right. INTRODUCTION Contract doctors in Malaysia held a strike on July 26, 2021. COVID-19 cases are increasing in Malaysia. In June, daily cases ranged between 4,000 to 8,000 despite various public health measures. The R naught, which indicates the infectiousness of COVID-19, remains unchanged. During the pandemic, health care workers (HCWs) have been widely celebrated, resulting in a renewed appreciation of the risks that they face.[1] The pandemic has exposed flawed governance in the public healthcare system, particularly surrounding the employment of contract doctors. Contract doctors in Malaysia are doctors who have completed their medical training, as well as two years of internship, and have subsequently been appointed as medical officers for another two years. Contract doctors are not permanently appointed, and the system did not allow extensions after the two years nor does it offer any opportunity to specialize.[2] Last week, Parliament did decide to offer a two-year extension but that did not hold off the impending strike.[3] In 2016, the Ministry of Health introduced a contract system to place medical graduates in internship positions at government healthcare facilities across the country rather than placing them in permanent posts in the Public Service Department. Social media chronicles the issues that doctors in Malaysia faced. However, tensions culminated when and contract doctors called for a strike which ended up taking place in late July 2021. BACKGROUND Over the past decade, HCW strikes have arisen mostly over wages, work hours, and administrative and financial factors.[4] In 2012, the British Medical Association organized a single “day of action” by boycotting non-urgent care as a response to government pension reforms.[5] In Ireland, doctors went on strike for a day in 2013 to protest the austerity measures implemented by the EU in response to the global economic crisis. It involved a dispute over long working hours (100 hours per week) which violated EU employment laws and more importantly put patients’ lives at risk.[6] The strike resulted in the cancellation of 15,000 hospital appointments, but emergencies services were continued. Other major strikes have been organized in the UK to negotiate better pay for HCWs in general and junior doctors’ contracts specifically.[7] During the COVID-19 pandemic, various strikes have also been organized in Hong Kong, the US, and Bolivia due to various pitfalls in managing the pandemic.[8] A recent strike in August 2020 by South Korean junior doctors and medical students was organized to protest a proposed medical reform plan which did not address wage stagnation and unfair labor practices.[9] These demands are somewhat similar to the proposed strike by contract doctors in Malaysia. As each national health system operates within a different setting, these strikes should be examined in detail to understand the degree of self-interest involved versus concerns for patient’s welfare. l. The Malaysia Strike An anonymous group planned the current strike in Malaysia. The group used social media, garnering the attention of various key stakeholders including doctors, patients, government, and medical councils.[10] The organizers of the strike referred to their planned actions as a hartal. (Although historically a hartal involved a total shutdown of workplaces, offices, shops, and other establishments as a form of civil disobedience, the Malaysian contract doctors pledged no disturbance to healthcare working hours or services and intend a walk-out that is symbolic and reflective of a strike.)[11] The call to action mainly involved showing support for the contract doctors with pictures and placards. The doctors also planned the walk-out.[12] Despite earlier employment, contract medical doctors face many inequalities as opposed to their permanent colleagues. These include differences in basic salary, provisions of leave, and government loans despite doing the same job. The system disadvantages contract doctors offering little to no job security and limited career progression. Furthermore, reports in 2020 showed that close to 4,000 doctors’ contracts were expected to expire by May 2022, leaving their futures uncertain.[13] Some will likely be offered an additional two years as the government faces pressure from the workers. Between December 2016 and May 2021, a total of 23,077 contract doctors were reportedly appointed as medical officers, with only 789 receiving permanent positions.[14] It has been suggested that they are appointed into permanent positions based on merit but the criteria for the appointments remain unclear. Those who fail to acquire a permanent position inevitably seek employment elsewhere. During the COVID-19 pandemic, there have been numerous calls for the government to absorb contract doctors into the public service as permanent staff with normal benefits. This is important considering a Malaysian study that revealed that during the pandemic over 50 percent of medical personnel feel burned out while on duty.[15] This effort might be side-lined as the government prioritizes curbing the pandemic. As these issues remain neglected, the call for a strike should be viewed as a cry for help to reignite the discussions about these issues. ll. Right to strike The right to strike is recognized as a fundamental human right by the UN and the EU.[16] Most European countries also protect the right to strike in their national constitutions.[17] In the US, the Taft-Hartley Act in 1947 prohibited healthcare workers of non-profit hospitals to form unions and engage in collective bargaining. But this exclusion was repealed in 1947 and replaced with the requirement of a 10-day advanced written notice prior to any strike action.[18] Similarly, Malaysia also recognizes the right to dispute over labor matters, either on an individual or collective basis. The Industrial Relations Act (IRA) of 1967[19] describes a strike as: “the cessation of work by a body of workers acting in combination, or a concerted refusal or a refusal under a common understanding of a number of workers to continue to work or to accept employment, and includes any act or omission by a body of workers acting in combination or under a common understanding, which is intended to or does result in any limitation, restriction, reduction or cessation of or dilatoriness in the performance or execution of the whole or any part of the duties connected with their employment” According to the same act, only members of a registered trade union may legally participate in a strike with prior registration from the Director-General of Trade Unions.[20] Under Section 43 of the IRA, any strike by essential services (including healthcare) requires prior notice of 42 days to their employer.[21] Upon receiving the notice, the employer is responsible for reporting the particulars to the Director-General of Industrial Relations to allow a “cooling-off” period and appropriate action. Employees are also protected from termination if permitted by the Director-General and strike is legalized. The Malaysian contract healthcare workers’ strike was announced and transparent. Unfortunately, even after legalization, there is fear that the government may charge those participating in the legalized strike.[22] The police have announced they will pursue participants in the strike.[23] Even the Ministry of Health has issued a warning stating that those participating in the strike may face disciplinary actions from the ministry. However, applying these laws while ignoring the underlying issues may not bode well for the COVID-19 healthcare crisis. lll. Effects of a Strike on Health Care There is often an assumption that doctors’ strikes would unavoidably cause significant harm to patients. However, a systematic review examining several strikes involving physicians reported that patient mortality remained the same or fell during the industrial action.[24] A study after the 2012 British Medical Association strike has even shown that there were fewer in-hospital deaths on the day, both among elective and emergency populations, although neither difference was significant.[25] Similarly, a recent study in Kenya showed declines in facility-based mortality during strike months.[26] Other studies have shown no obvious changes in overall mortality during strikes by HCWs.[27] There is only one report of increased mortality associated with a strike in South Africa[28] in which all the doctors in the Limpopo province stopped providing any treatment to their patients for 20 consecutive days. During this time, only one hospital continued providing services to a population of 5.5 million people. Even though their data is incomplete, authors from this study found that the number of emergency room visits decreased during the strike, but the risks of mortality in the hospital for these patients increased by 67 percent.[29] However, the study compared the strike period to a randomly selected 20-day period in May rather than comparing an average of data taken from similar dates over previous years. This could greatly influence variations between expected annual hospital mortality possibly due to extremes in weather that may exacerbate pre-existing conditions such as heart failure during warmer months or selecting months with a higher incidence of viral illness such as influenza. Importantly, all strikes ensured that emergency services were continued, at least to the degree that is generally offered on weekends. Furthermore, many doctors still provide usual services to patients despite a proclaimed strike. For example, during the 2012 BMA strike, less than one-tenth of doctors were estimated to be participating in the strike.[30] Emergency care may even improve during strikes, especially those involving junior doctors who are replaced by more senior doctors.[31] The cancellation of elective surgeries may also increase the number of doctors available to treat emergency patients. Furthermore, the cancellation of elective surgery is likely to be responsible for transient decreases in mortality. Doctors also may get more rest during strike periods. Although doctor strikes do not seem to increase patient mortality, they can disrupt delivery of healthcare.[32] Disruptions in delivery of service from prolonged strikes can result in decline of in-patient admissions and outpatient service utilization, as suggested during strikes in the UK in 2016.[33] When emergency services were affected during the last strike in April, regular service was also significantly affected. Additionally, people might need to seek alternative sources of care from the private sector and face increased costs of care. HCWs themselves may feel guilty and demotivated because of the strikes. The public health system may also lose trust as a result of service disruption caused by high recurrence of strikes. During the COVID-19 pandemic, as the healthcare system remains stretched, the potential adverse effects resulting from doctor strikes remain uncertain and potentially disruptive. In the UK, it is an offence to “willfully and maliciously…endanger human life or cause serious bodily injury.”[34] Likewise, the General Medical Council (GMC) also requires doctors to ensure that patients are not harmed or put at risk by industrial action. In the US, the American Medical Association code of ethics prohibits strikes by physicians as a bargaining tactic, while allowing some other forms of collective bargaining.[35] However, the American College of Physicians prohibits all forms of work stoppages, even when undertaken for necessary changes to the healthcare system. Similarly, the Delhi Medical Council in India issued a statement that “under no circumstances doctors should resort to strike as the same puts patient care in serious jeopardy.”[36] On the other hand, the positions taken by the Malaysian Medical Council (MMC) and Malaysian Medical Association (MMA) on doctors’ strikes are less clear when compared to their Western counterparts. The MMC, in their recently updated Code of Professional Conduct 2019, states that “the public reputation of the medical profession requires that every member should observe proper standards of personal behavior, not only in his professional activities but at all times.” Strikes may lead to imprisonment and disciplinary actions by MMC for those involved. Similarly, the MMA Code of Medical Ethics published in 2002 states that doctors must “make sure that your personal beliefs do not prejudice your patients' care.”[37] The MMA which is traditionally meant to represent the voices of doctors in Malaysia, may hold a more moderate position on strikes. Although HCW strikes are not explicitly mentioned in either professional body’s code of conduct and ethics, the consensus is that doctors should not do anything that will harm patients and they must maintain the proper standard of behaviors. These statements seem too general and do not represent the complexity of why and how a strike could take place. Therefore, it has been suggested that doctors and medical organizations should develop a new consensus on issues pertaining to medical professional’s social contract with society while considering the need to uphold the integrity of the profession. Experts in law, ethics, and medicine have long debated whether and when HCW strikes can be justified. If a strike is not expected to result in patient harm it is perhaps acceptable.[38] Although these debates have centered on the potential risks that strikes carry for patients, these actions also pose risks for HCWs as they may damage morale and reputation.[39] Most fundamentally, strikes raise questions about what healthcare workers owe society and what society owes them. For strikes to be morally permissible and ethical, it is suggested that they must fulfil these three criteria:[40] a. Strikes should be proportionate, e., they ‘should not inflict disproportionate harm on patients’, and hospitals should as a minimum ‘continue to provide at least such critical services as emergency care.’ b. Strikes should have a reasonable hope of success, at least not totally futile however tough the political rhetoric is. c. Strikes should be treated as a last resort: ‘all less disruptive alternatives to a strike action must have been tried and failed’, including where appropriate ‘advocacy, dissent and even disobedience’. The current strike does not fulfil the criteria mentioned. As Malaysia is still burdened with a high number of COVID-19 cases, a considerable absence of doctors from work will disrupt health services across the country. Second, since the strike organizer is not unionized, it would be difficult to negotiate better terms of contract and career paths. Third, there are ongoing talks with MMA representing the fraternity and the current government, but the time is running out for the government to establish a proper long-term solution for these contract doctors. One may argue that since the doctors’ contracts will end in a few months with no proper pathways for specialization, now is the time to strike. However, the HCW right to strike should be invoked only legally and appropriately after all other options have failed. CONCLUSION The strike in Malaysia has begun since the drafting of this paper. Doctors involved assure that there will not be any risk to patients, arguing that the strike is “symbolic”.[41] Although an organized strike remains a legal form of industrial action, a strike by HCWs in Malaysia poses various unprecedented challenges and ethical dilemmas, especially during the pandemic. The anonymous and uncoordinated strike without support from the appropriate labor unions may only spark futile discussions without affirmative actions. It should not have taken a pandemic or a strike to force the government to confront the issues at hand. It is imperative that active measures be taken to urgently address the underlying issues relating to contract physicians. As COVID-19 continues to affect thousands of people, a prompt reassessment is warranted regarding the treatment of HCWs, and the value placed on health care. [1] Ministry of Health (MOH) Malaysia, “Current situation of COVID-19 in Malaysia.” http://covid-19.moh.gov.my/terkini (accessed Jul. 01, 2021). [2] “Future of 4,000 young doctors who are contract medical officers uncertain,” New Straits Times - November 26, 2020. https://www.nst.com.my/news/nation/2020/11/644563/future-4000-young-doctors-who-are-contract-medical-officers-uncertain [3] “Malaysia doctors strike, parliament meets as COVID strain shows,” Al Jazeera, July 26, 2021. https://www.aljazeera.com/news/2021/7/26/malaysia-doctors-strike-parliament-meets-as-covid-strains-grow [4] R. Essex and S. M. Weldon, “Health Care Worker Strikes and the Covid Pandemic,” N. Engl. J. Med., vol. 384, no. 24, p. e93, Jun. 2021, doi: 10.1056/NEJMp2103327; G. Russo et al., “Health workers’ strikes in low-income countries: the available evidence,” Bull. World Health Organ., vol. 97, no. 7, pp. 460-467H, Jul. 2019, doi: 10.2471/BLT.18.225755. [5] M. Ruiz, A. Bottle, and P. Aylin, “A retrospective study of the impact of the doctors’ strike in England on 21 June 2012,” J. R. Soc. Med., vol. 106, no. 9, pp. 362–369, 2013, doi: 10.1177/0141076813490685. [6] E. Quinn, “Irish Doctors Strike to Protest Work Hours Amid Austerity,” The Wall Street Journal, 2013. https://www.wsj.com/articles/no-headline-available-1381217911?tesla=y (accessed Jun. 29, 2021). [7] “NHS workers back strike action in pay row by 2-to-1 margin,” The Guardian, 2014. https://www.theguardian.com/society/2014/sep/18/nhs-workers-strike-pay-unison-england (accessed Jun. 29, 2021); M. Limb, “Thousands of junior doctors march against new contract,” BMJ, p. h5572, Oct. 2015, doi: 10.1136/bmj.h5572. [8] J. Parry, “China coronavirus: Hong Kong health staff strike to demand border closure as city records first death,” BMJ, vol. 368, no. February, p. m454, Feb. 2020, doi: 10.1136/bmj.m454; “MultiCare healthcare workers strike, urging need for more PPEs, staff support,” Q13 FOX, 2020. https://www.q13fox.com/news/health-care-workers-strike-urging-need-for-ppes-risks-on-patient-safety (accessed Jun. 29, 2021); “Bolivia healthcare workers launch strike in COVID-hit region,” Al Jazeera, 2021. https://www.aljazeera.com/news/2021/2/9/bolivia-healthcare-workers-strike-covid-hit-region (accessed Jun. 29, 2021). [9] K. Arin, “Why are Korean doctors striking?” The Korea Herald, 2020. http://www.koreaherald.com/view.php?ud=20200811000941 (accessed Jun. 29, 2021). [10] “Hartal Doktor Kontrak,” Facebook. https://www.facebook.com/hartaldoktorkontrak. [11] “Hartal,” Oxford Advanced Learner’s Dictionary. https://www.oxfordlearnersdictionaries.com/definition/english/hartal (accessed Jun. 29, 2021). [12] “Hartal Doktor Kontrak,” Facebook. https://www.facebook.com/hartaldoktorkontrak. [13] R. Anand, “Underpaid and overworked, Malaysia’s contract doctors’ revolt amid Covid-19 surge,” The Straits Times, 2021. [14] Anand. [15] N. S. Roslan, M. S. B. Yusoff, A. R. Asrenee, and K. Morgan, “Burnout prevalence and its associated factors among Malaysian healthcare workers during covid-19 pandemic: An embedded mixed-method study,” Healthc., vol. 9, no. 1, 2021, doi: 10.3390/healthcare9010090. [16] Maina Kiai, “Report by the Special Rapporteur on the Right to Freedom of Peaceful Assembly and Association,” 2016. [Online]. Available: http://freeassembly.net/wp-content/uploads/2016/10/A.71.385_E.pdf. [17] ETUI contributors, Strike rules in the EU27 and beyond. The European Trade Union Institute. ETUI, 2007. [18] National Labor Relations Board, National Labor Relations Act. 1935, pp. 151–169. [19] Ministry of Human Resources, Industrial Relations Act 1967 (Act 177), no. October. 2015, pp. 1–76. [20] Article 10 of the Federal Constitution states that all citizens have the right to form associations including registered trade or labor unions. A secret ballot with two-third majority will suffice to call for a strike required for submission to the DGTU within 7 days as stated in Section 25(A) of the Trade Union Act 1959. [21] Ministry of Human Resources Malaysia, Guidelines on Strikes, Pickets and Lockouts in Malaysia. Putrajaya, 2011. [22] Ordinance Emergency which was declared in Malaysia since 12 January 2021. Under the Ordinance Emergency, the king or authorized personnel may, as deemed necessary, demand any resources. [23] “Malaysia doctors strike, parliament meets as COVID strain shows,” Al Jazeera, July 26, 2021. https://www.aljazeera.com/news/2021/7/26/malaysia-doctors-strike-parliament-meets-as-covid-strains-grow [24] S. A. Cunningham, K. Mitchell, K. M. Venkat Narayan, and S. Yusuf, “Doctors’ strikes and mortality: A review,” Soc. Sci. Med., vol. 67, no. 11, pp. 1784–1788, Dec. 2008, doi: 10.1016/j.socscimed.2008.09.044. [25] M. Ruiz, A. Bottle, and P. Aylin, “A retrospective study of the impact of the doctors’ strike in England on 21 June 2012,” J. R. Soc. Med., vol. 106, no. 9, pp. 362–369, 2013, doi: 10.1177/0141076813490685. [26] G. K. Kaguthi, V. Nduba, and M. B. Adam, “The impact of the nurses’, doctors’ and clinical officer strikes on mortality in four health facilities in Kenya,” BMC Health Serv. Res., vol. 20, no. 1, p. 469, Dec. 2020, doi: 10.1186/s12913-020-05337-9. [27] G. Ong’ayo et al., “Effect of strikes by health workers on mortality between 2010 and 2016 in Kilifi, Kenya: a population-based cohort analysis,” Lancet Glob. Heal., vol. 7, no. 7, pp. e961–e967, Jul. 2019, doi: 10.1016/S2214-109X (19)30188-3. [28] M. M. Z. U. Bhuiyan and A. Machowski, “Impact of 20-day strike in Polokwane Hospital (18 August - 6 September 2010),” South African Med. J., vol. 102, no. 9, p. 755, Aug. 2012, doi: 10.7196/SAMJ.6045. [29] M. M. Z. U. Bhuiyan and A. Machowski, “Impact of 20-day strike in Polokwane Hospital (18 August - 6 September 2010),” South African Med. J., vol. 102, no. 9, p. 755, Aug. 2012, doi: 10.7196/SAMJ.6045. [30] M. Ruiz, A. Bottle, and P. Aylin, “A retrospective study of the impact of the doctors’ strike in England on 21 June 2012,” J. R. Soc. Med., vol. 106, no. 9, pp. 362–369, 2013, doi: 10.1177/0141076813490685. [31] D. Metcalfe, R. Chowdhury, and A. Salim, “What are the consequences when doctors strike?” BMJ, vol. 351, no. November, pp. 1–4, 2015, doi: 10.1136/bmj.h6231. [32] D. Waithaka et al., “Prolonged health worker strikes in Kenya- perspectives and experiences of frontline health managers and local communities in Kilifi County,” Int. J. Equity Health, vol. 19, no. 1, pp. 1–15, 2020, doi: 10.1186/s12939-020-1131-y. [33] The study has shown that there were 9.1% reduction in admissions and around 6% fewer emergency cases and outpatient appointments than expected. An additional 52% increase in expected outpatient appointments cancelations were made by hospitals during that period. D. Furnivall, A. Bottle, and P. Aylin, “Retrospective analysis of the national impact of industrial action by English junior doctors in 2016,” BMJ Open, vol. 8, no. 1, p. e019319, Jan. 2018, doi: 10.1136/bmjopen-2017-019319. [34] D. Metcalfe, R. Chowdhury, and A. Salim, “What are the consequences when doctors strike?” BMJ, vol. 351, no. November, pp. 1–4, 2015, doi: 10.1136/bmj.h6231. [35] R. Essex and S. M. Weldon, “Health Care Worker Strikes and the Covid Pandemic,” N. Engl. J. Med., vol. 384, no. 24, p. e93, Jun. 2021, doi: 10.1056/NEJMp2103327. [36] M. Selemogo, “Criteria for a just strike action by medical doctors,” Indian J. Med. Ethics, vol. 346, no. 21, pp. 1609–1615, Jan. 2014, doi: 10.20529/IJME.2014.010. [37] Malaysian Medical Association, “Malaysian Medical Association Official Website.” https://mma.org.my (accessed Jun. 29, 2021). [38] M. Toynbee, A. A. J. Al-Diwani, J. Clacey, and M. R. Broome, “Should junior doctors strike?” J. Med. Ethics, vol. 42, no. 3, pp. 167–170, Mar. 2016, doi: 10.1136/medethics-2015-103310. [39] R. Essex and S. M. Weldon, “Health Care Worker Strikes and the Covid Pandemic,” N. Engl. J. Med., vol. 384, no. 24, p. e93, Jun. 2021, doi: 10.1056/NEJMp2103327. [40] M. Selemogo, “Criteria for a just strike action by medical doctors,” Indian J. Med. Ethics, vol. 346, no. 21, pp. 1609–1615, Jan. 2014, doi: 10.20529/IJME.2014.010; A. J. Roberts, “A framework for assessing the ethics of doctors’ strikes,” J. Med. Ethics, vol. 42, no. 11, pp. 698–700, Nov. 2016, doi: 10.1136/medethics-2016-103395. [41] “Malaysia doctors strike, parliament meets as COVID strain shows,” Al Jazeera, July 26, 2021. https://www.aljazeera.com/news/2021/7/26/malaysia-doctors-strike-parliament-meets-as-covid-strains-grow

&ldquo;#167 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). @ResearchGate: https://www.researchgate.net/publication/368753609 &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperK-Number). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperK-Number if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$&nbsp;&nbsp;&nbsp; Neutrosophic re-SuperHyperK-Number if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperK-Number if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$ Neutrosophic rv-SuperHyperK-Number if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$&nbsp;&nbsp; Neutrosophic SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number. ((Neutrosophic) SuperHyperK-Number). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; a Neutrosophic SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; an Extreme SuperHyperK-Number SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; a Neutrosophic V-SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; an Extreme V-SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperK-Number &nbsp;and Neutrosophic SuperHyperK-Number. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperK-Number is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperK-Number is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperK-Number . Since there&#39;s more ways to get type-results to make a SuperHyperK-Number &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperK-Number, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperK-Number &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperK-Number . It&#39;s redefined a Neutrosophic SuperHyperK-Number &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperK-Number . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperK-Number until the SuperHyperK-Number, then it&#39;s officially called a ``SuperHyperK-Number&#39;&#39; but otherwise, it isn&#39;t a SuperHyperK-Number . There are some instances about the clarifications for the main definition titled a ``SuperHyperK-Number &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperK-Number . For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperK-Number&#39;&#39; and a ``Neutrosophic SuperHyperK-Number &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperK-Number &nbsp;are redefined to a ``Neutrosophic SuperHyperK-Number&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperK-Number &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperK-Number&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperK-Number&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperK-Number &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperK-Number .] SuperHyperK-Number . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperK-Number if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperK-Number &nbsp;or the strongest SuperHyperK-Number &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperK-Number, called SuperHyperK-Number, and the strongest SuperHyperK-Number, called Neutrosophic SuperHyperK-Number, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Number. There isn&#39;t any formation of any SuperHyperK-Number but literarily, it&#39;s the deformation of any SuperHyperK-Number. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperK-Number theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperK-Number, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Number&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperK-Number or the Extreme&nbsp;&nbsp; SuperHyperK-Number in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Number. There isn&#39;t any formation of any SuperHyperK-Number but literarily, it&#39;s the deformation of any SuperHyperK-Number. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperK-Number&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperK-Number and Extreme&nbsp;&nbsp; SuperHyperK-Number, are figured out in sections ``&nbsp; SuperHyperK-Number&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperK-Number&#39;&#39;. In the sense of tackling on getting results and in K-Number to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperK-Number&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperK-Number&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperK-Number&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Numbered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Numbered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let an K-Numbered pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperK-Number} if&nbsp; $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperK-Number} if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperK-Number} if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperK-Number} if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperK-Number} is a Neutrosophic kind of Neutrosophic SuperHyperK-Number such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperK-Number} is a Neutrosophic kind of Neutrosophic SuperHyperK-Number such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperK-Number. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperK-Number more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperK-Number&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperK-Number. It&#39;s redefined a \textbf{Neutrosophic SuperHyperK-Number} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperK-Number But As The Extensions Excerpt From Dense And Super Forms} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperK-Number. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=2z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperK-Number. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i\neq2,5}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=4z^3. &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=4z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_3,O\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =5\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \ldots &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i=1}^{10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=z^{10}. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=|E_{NSHG}|~\text{choose two}z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=\text{four choose three}z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3,E_4\}. &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z. &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \ldots &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=1}^{|V_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{|V_{NSHG}|}. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{22}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^{22}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^{22}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Quasi-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{17}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{17}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{4}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{4}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{23}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^{23}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^{22}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Quasi-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{7}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{7}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{{E_i}_{i=1}^8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^8. &nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^6. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp; =\{V_i\}_{i\neq 4,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =2\times2\times2\times2\times2z^5. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp; =\{{V_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{{E_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^{10}. &nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}= z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}= 2z^2. &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{V_2,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{29}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{29}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^6. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{29}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{29}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{12}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{12}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{{V_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{11}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{11}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=10z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{10}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{2}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{2}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Number, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{5}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{5}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =5z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;\\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperK-Number in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;\\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E_i\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. Then there&#39;s no at least one SuperHyperK-Number. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Number could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Number taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Number in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} is a longest SuperHyperK-Number taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperK-Number. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Number could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperK-Number in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperK-Number taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. Then there&#39;s at least one SuperHyperK-Number. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperK-Number could be applied. The unique embedded SuperHyperK-Number proposes some longest SuperHyperK-Number excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Number in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperK-Number,&nbsp; Extreme SuperHyperK-Number, and the Extreme SuperHyperK-Number, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperK-Number is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperK-Number. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperK-Number=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperK-Number of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperK-Number \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperK-Number.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperK-Number and SuperHyperK-Number coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperK-Number if and only if it&#39;s a SuperHyperK-Number. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperK-Number if and only if it&#39;s a longest SuperHyperK-Number. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperK-Number is its SuperHyperK-Number and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperK-Number is its SuperHyperK-Number and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Number/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Number/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperK-Number; &nbsp; \item[$(ii):$] the SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperK-Number. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperK-Number; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperK-Number. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperK-Number/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Number, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Number, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperK-Number set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperK-Number. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperK-Number. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperK-Number; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperK-Number, then $S$ is an s-SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Number, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperK-Number, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Number, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperK-Number. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperK-Number. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperK-Number or the Extreme&nbsp;&nbsp; SuperHyperK-Number in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperK-Number} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperK-Number. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperK-Number} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperK-Number. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperK-Number and the Extreme&nbsp;&nbsp; SuperHyperK-Number are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperK-Number and the Extreme&nbsp;&nbsp; SuperHyperK-Number? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperK-Number and the Extreme&nbsp;&nbsp; SuperHyperK-Number? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperK-Number and the Extreme&nbsp;&nbsp; SuperHyperK-Number do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperK-Number, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperK-Number. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperK-Number, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperK-Number, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperK-Number and the Extreme&nbsp;&nbsp; SuperHyperK-Number. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Number&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperK-Number}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperK-Number}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperDuality).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperJoin).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperPerfect).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ ExtremeSuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperTotal).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperConnected).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, K-Number, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Number alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022),&nbsp; there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperDominating, Neutrosophic SuperHyperDominating theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG162}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Number alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&#39;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperK-Number As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperK-Number In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#169 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). @ResearchGate: https://www.researchgate.net/publication/368786722 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperK-Domination). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperK-Domination if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$&nbsp;&nbsp;&nbsp; Neutrosophic re-SuperHyperK-Domination if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperK-Domination if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$ Neutrosophic rv-SuperHyperK-Domination if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$&nbsp;&nbsp; Neutrosophic SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination. ((Neutrosophic) SuperHyperK-Domination). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; a Neutrosophic SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; an Extreme SuperHyperK-Domination SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; a Neutrosophic V-SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; an Extreme V-SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperK-Domination &nbsp;and Neutrosophic SuperHyperK-Domination. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperK-Domination is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperK-Domination is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperK-Domination . Since there&#39;s more ways to get type-results to make a SuperHyperK-Domination &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperK-Domination &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperK-Domination . It&#39;s redefined a Neutrosophic SuperHyperK-Domination &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperK-Domination . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperK-Domination until the SuperHyperK-Domination, then it&#39;s officially called a ``SuperHyperK-Domination&#39;&#39; but otherwise, it isn&#39;t a SuperHyperK-Domination . There are some instances about the clarifications for the main definition titled a ``SuperHyperK-Domination &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperK-Domination . For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperK-Domination&#39;&#39; and a ``Neutrosophic SuperHyperK-Domination &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperK-Domination &nbsp;are redefined to a ``Neutrosophic SuperHyperK-Domination&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperK-Domination &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperK-Domination&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperK-Domination&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperK-Domination &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperK-Domination .] SuperHyperK-Domination . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperK-Domination if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperK-Domination &nbsp;or the strongest SuperHyperK-Domination &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperK-Domination, called SuperHyperK-Domination, and the strongest SuperHyperK-Domination, called Neutrosophic SuperHyperK-Domination, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Domination. There isn&#39;t any formation of any SuperHyperK-Domination but literarily, it&#39;s the deformation of any SuperHyperK-Domination. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperK-Domination theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperK-Domination, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Domination&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperK-Domination or the Extreme&nbsp;&nbsp; SuperHyperK-Domination in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Domination. There isn&#39;t any formation of any SuperHyperK-Domination but literarily, it&#39;s the deformation of any SuperHyperK-Domination. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperK-Domination&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperK-Domination and Extreme&nbsp;&nbsp; SuperHyperK-Domination, are figured out in sections ``&nbsp; SuperHyperK-Domination&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39;. In the sense of tackling on getting results and in K-Domination to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperK-Domination&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperK-Domination&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Dominationed pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Dominationed pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let an K-Dominationed pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperK-Domination} if&nbsp; $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperK-Domination} if $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperK-Domination} if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperK-Domination} if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperK-Domination} is a Neutrosophic kind of Neutrosophic SuperHyperK-Domination such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperK-Domination} is a Neutrosophic kind of Neutrosophic SuperHyperK-Domination such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperK-Domination. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperK-Domination more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperK-Domination&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperK-Domination. It&#39;s redefined a \textbf{Neutrosophic SuperHyperK-Domination} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperK-Domination But As The Extensions Excerpt From Dense And Super Forms} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperK-Domination. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=2z. &nbsp;&nbsp;&nbsp; \\&amp;&amp; E_4\sim E_2\rightarrow 2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; V_4\sim V_2,V_1\rightarrow 3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperK-Domination. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}=z^4. &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \text{[Two SuperHyperVertices are dominated by all non-isolated elements inside.]} \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_i\}_{i\neq2,5}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=4z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_3,O\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^6. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=4z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^{14}. &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^7. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^6. \end{eqnarray*} \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^{11}. &nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^6. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^6. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^6. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp; =\{V_i\}_{i\neq 4,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =2\times2\times2\times2\times2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^6. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^3. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}}= z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}}=\{V_2,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^{14}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^{14}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{{V_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^9. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{|V_{NSHG}|-1}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperK-Domination, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =5z^{16}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;\\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^s. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperK-Domination in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;\\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E_i\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{|V_{NSHG}|-1}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. Then there&#39;s no at least one SuperHyperK-Domination. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Domination could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Domination taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Domination in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} is a longest SuperHyperK-Domination taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperK-Domination. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Domination could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperK-Domination in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination}}=\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|-1}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{|V^{*}_{NSHG}|-1}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperK-Domination taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. Then there&#39;s at least one SuperHyperK-Domination. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperK-Domination could be applied. The unique embedded SuperHyperK-Domination proposes some longest SuperHyperK-Domination excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperK-Domination in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperK-Domination,&nbsp; Extreme SuperHyperK-Domination, and the Extreme SuperHyperK-Domination, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperK-Domination is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperK-Domination. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperK-Domination=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperK-Domination of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperK-Domination \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperK-Domination.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperK-Domination and SuperHyperK-Domination coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperK-Domination if and only if it&#39;s a SuperHyperK-Domination. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperK-Domination if and only if it&#39;s a longest SuperHyperK-Domination. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperK-Domination is its SuperHyperK-Domination and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperK-Domination is its SuperHyperK-Domination and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Domination/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Domination/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperK-Domination; &nbsp; \item[$(ii):$] the SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperK-Domination; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperK-Domination/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Domination, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Domination, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperK-Domination set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperK-Domination. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperK-Domination. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperK-Domination; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is an s-SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperK-Domination, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperK-Domination. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperK-Domination. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperK-Domination or the Extreme&nbsp;&nbsp; SuperHyperK-Domination in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperK-Domination} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperK-Domination. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperK-Domination} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperK-Domination. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperK-Domination and the Extreme&nbsp;&nbsp; SuperHyperK-Domination are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperK-Domination and the Extreme&nbsp;&nbsp; SuperHyperK-Domination? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperK-Domination and the Extreme&nbsp;&nbsp; SuperHyperK-Domination? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperK-Domination and the Extreme&nbsp;&nbsp; SuperHyperK-Domination do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperK-Domination, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperK-Domination. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperK-Domination, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperK-Domination, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperK-Domination and the Extreme&nbsp;&nbsp; SuperHyperK-Domination. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Domination&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperK-Domination}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperK-Domination}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperDuality).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperDuality} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperDuality, Extremere-SuperHyperDuality, Extremev-SuperHyperDuality, and Extremerv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperDuality; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperDuality, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperDuality. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperJoin).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperJoin} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperJoin, Extremere-SuperHyperJoin, Extremev-SuperHyperJoin, and Extremerv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperJoin; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperJoin, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperJoin. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperPerfect).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperPerfect} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperPerfect, Extremere-SuperHyperPerfect, Extremev-SuperHyperPerfect, and Extremerv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperPerfect; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperPerfect, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperPerfect. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ ExtremeSuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperTotal).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperTotal} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperTotal, Extremere-SuperHyperTotal, Extremev-SuperHyperTotal, and Extremerv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperTotal; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperTotal, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperTotal. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{ExtremeCardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ ExtremeSuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different ExtremeTypes of ExtremeSuperHyperConnected).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extremee-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extremere-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extremev-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extremerv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{ExtremeSuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider an ExtremeSuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{ExtremeSuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality&nbsp; consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{ExtremeSuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperEdges of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; and the Extremepower is corresponded to its Extremecoefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{ExtremeR-SuperHyperConnected} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{ExtremeSuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extremee-SuperHyperConnected, Extremere-SuperHyperConnected, Extremev-SuperHyperConnected, and Extremerv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an ExtremeSuperHyperGraph $NSHG:(V,E)$ is&nbsp; the ExtremeSuperHyperPolynomial contains the Extremecoefficients defined as the Extremenumber of the maximum Extremecardinality of the ExtremeSuperHyperVertices of an ExtremeSuperHyperSet $S$ of high Extremecardinality consecutive ExtremeSuperHyperEdges and ExtremeSuperHyperVertices such that they form the ExtremeSuperHyperConnected; and the Extremepower is corresponded to its Extremecoefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an ExtremeSuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned ExtremeFigures in every Extremeitems. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp;SuperHyperEdges but $E_2$ is a loop ExtremeSuperHyperEdge and $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty ExtremeSuperHyperEdges but $E_4$ is an ExtremeSuperHyperEdge. Thus in the terms of ExtremeSuperHyperNeighbor, there&#39;s only one ExtremeSuperHyperEdge, namely, $E_4.$ The ExtremeSuperHyperVertex, $V_3$ is Extremeisolated means that there&#39;s no ExtremeSuperHyperEdge has it as an Extremeendpoint. Thus the ExtremeSuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given ExtremeSuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the ExtremeSuperHyperNotion, namely, ExtremeSuperHyperConnected, is up. The ExtremeAlgorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extremeapproach apply on the upcoming Extremeresults on ExtremeSuperHyperClasses. \begin{proposition} Assume a connected ExtremeSuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected ExtremeSuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected ExtremeSuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The ExtremeSuperHyperSet,&nbsp; in the ExtremeSuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{ExtremeR-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{ExtremeR-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected ExtremeSuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected ExtremeSuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, in the ExtremeSuperHyperModel \eqref{136NSHG19a}, is the Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeR-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected ExtremeSuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected ExtremeSuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the&nbsp; ExtremeSuperHyperVertices of the connected ExtremeSuperHyperStar $ESHS:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG20a}, is the&nbsp; ExtremeSuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the ExtremeFigure \eqref{136NSHG21a}, the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ is Extremehighlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the ExtremeAlgorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperBipartite $ESHB:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG21a}, is the Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeQuasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{ExtremeCardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; ExtremeSuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extremefeatured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous Extremeresult, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperMultipartite $ESHM:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG22a}, is the&nbsp; ExtremeSuperHyperConnected. \end{example} \begin{proposition} Assume a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeSuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{ExtremeCardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{ExtremeV-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected ExtremeSuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the ExtremeFigure \eqref{136NSHG23a}, the connected ExtremeSuperHyperWheel $NSHW:(V,E),$ is Extremehighlighted and featured. The obtained ExtremeSuperHyperSet, by the Algorithm in previous result, of the ExtremeSuperHyperVertices of the connected ExtremeSuperHyperWheel $ESHW:(V,E),$ in the ExtremeSuperHyperModel \eqref{136NSHG23a}, is the&nbsp; ExtremeSuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, K-Domination, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Domination alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022),&nbsp; there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperDominating, Neutrosophic SuperHyperDominating theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG162}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Domination alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&#39;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperK-Domination As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperK-Domination In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document} &nbsp;

&ldquo;#170 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). @ResearchGate: https://www.researchgate.net/publication/368781100 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; &nbsp; &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperK-Domination). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Domination pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperK-Domination if&nbsp; $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$&nbsp;&nbsp;&nbsp; Neutrosophic re-SuperHyperK-Domination if $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperK-Domination if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$ Neutrosophic rv-SuperHyperK-Domination if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$&nbsp; Neutrosophic SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination. ((Neutrosophic) SuperHyperK-Domination). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; a Neutrosophic SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; an Extreme SuperHyperK-Domination SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; a Neutrosophic V-SuperHyperK-Domination if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; an Extreme V-SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Domination SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperK-Domination &nbsp;and Neutrosophic SuperHyperK-Domination. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperK-Domination is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperK-Domination is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperK-Domination . Since there&#39;s more ways to get type-results to make a SuperHyperK-Domination &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperK-Domination &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperK-Domination . It&#39;s redefined a Neutrosophic SuperHyperK-Domination &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperK-Domination . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperK-Domination until the SuperHyperK-Domination, then it&#39;s officially called a ``SuperHyperK-Domination&#39;&#39; but otherwise, it isn&#39;t a SuperHyperK-Domination . There are some instances about the clarifications for the main definition titled a ``SuperHyperK-Domination &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperK-Domination . For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperK-Domination&#39;&#39; and a ``Neutrosophic SuperHyperK-Domination &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperK-Domination &nbsp;are redefined to a ``Neutrosophic SuperHyperK-Domination&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperK-Domination &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperK-Domination&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperK-Domination&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperK-Domination &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperK-Domination .] SuperHyperK-Domination . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperK-Domination if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperK-Domination &nbsp;or the strongest SuperHyperK-Domination &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperK-Domination, called SuperHyperK-Domination, and the strongest SuperHyperK-Domination, called Neutrosophic SuperHyperK-Domination, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Domination. There isn&#39;t any formation of any SuperHyperK-Domination but literarily, it&#39;s the deformation of any SuperHyperK-Domination. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperK-Domination theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperK-Domination, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Domination&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperK-Domination or the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Domination. There isn&#39;t any formation of any SuperHyperK-Domination but literarily, it&#39;s the deformation of any SuperHyperK-Domination. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperK-Domination&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperK-Domination and Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination, are figured out in sections ``&nbsp; SuperHyperK-Domination&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39;. In the sense of tackling on getting results and in K-Domination to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperK-Domination&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperK-Domination&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Dominationed pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Dominationed pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let an K-Dominationed pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperK-Domination} if&nbsp; $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperK-Domination} if $\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_1,V_2,\ldots,V_k\in V,$ such that $V_1,V_2,\ldots,V_k\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperK-Domination} if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperK-Domination} if $\forall V_a\in E_{NSHG}\setminus E&#39;,~\exists V_b\in E&#39;,\exists E_1,E_2,\ldots,E_k\in E,$ such that $V_a,V_b\in E_1,E_2,\ldots,E_k;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperK-Domination} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Domination; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Domination, Neutrosophic re-SuperHyperK-Domination, Neutrosophic v-SuperHyperK-Domination, and Neutrosophic rv-SuperHyperK-Domination and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Domination; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperK-Domination).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperK-Domination} is a Neutrosophic kind of Neutrosophic SuperHyperK-Domination such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperK-Domination} is a Neutrosophic kind of Neutrosophic SuperHyperK-Domination such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperK-Domination. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperK-Domination more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperK-Domination, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperK-Domination&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperK-Domination. It&#39;s redefined a \textbf{Neutrosophic SuperHyperK-Domination} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperK-Domination But As The Extensions Excerpt From Dense And Super Forms} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperK-Domination. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=2z. \\&amp;&amp; E_4\sim E_2\rightarrow 2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; V_4\sim V_2,V_1\rightarrow 3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperK-Domination. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \text{[Two SuperHyperVertices are dominated by all non-isolated elements inside.]} \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}}=3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_i\}_{i\neq2,5}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=4z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_3,O\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=4z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^4. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Quasi-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^7. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^4. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Quasi-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^6. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^6. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp; =\{V_i\}_{i\neq 4,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =2\times2\times2\times2\times2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^6. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^3. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}}= z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}}=\{V_2,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; =z^{14}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^{14}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{{V_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^9. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{|V_{NSHG}|-1}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Domination, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =5z^{16}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^s. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}_{{i=0}}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E_i\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{|V_{NSHG}|-1}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. Then there&#39;s no at least one SuperHyperK-Domination. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Domination could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Domination taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\max_{P_j\in E_{NSHG}}|P_j|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Domination taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperK-Domination. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Domination could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination}}=\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Domination SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|-1}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Domination}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Domination SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{|V^{*}_{NSHG}|-1}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperK-Domination taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Domination. The latter is straightforward. Then there&#39;s at least one SuperHyperK-Domination. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperK-Domination could be applied. The unique embedded SuperHyperK-Domination proposes some longest SuperHyperK-Domination excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperK-Domination. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Domination in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperK-Domination,&nbsp; Neutrosophic SuperHyperK-Domination, and the Neutrosophic SuperHyperK-Domination, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperK-Domination is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperK-Domination. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperK-Domination=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperK-Domination of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperK-Domination \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperK-Domination.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperK-Domination and SuperHyperK-Domination coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperK-Domination if and only if it&#39;s a SuperHyperK-Domination. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperK-Domination if and only if it&#39;s a longest SuperHyperK-Domination. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperK-Domination is its SuperHyperK-Domination and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperK-Domination is its SuperHyperK-Domination and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperK-Domination isn&#39;t well-defined if and only if its SuperHyperK-Domination isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperK-Domination is well-defined if and only if its SuperHyperK-Domination is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Domination/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Domination; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Domination; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Domination/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperK-Domination; &nbsp; \item[$(ii):$] the SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperK-Domination; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Domination. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperK-Domination/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Domination, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Domination, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperK-Domination set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperK-Domination. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperK-Domination. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperK-Domination; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperK-Domination; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Domination for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperK-Domination for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is an s-SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperK-Domination, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Domination, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperK-Domination. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperK-Domination. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Domination. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Domination, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination or the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperK-Domination} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperK-Domination. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperK-Domination} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperK-Domination. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperK-Domination and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperK-Domination and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperK-Domination and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperK-Domination and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperK-Domination, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperK-Domination. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperK-Domination, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperK-Domination and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Domination&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperK-Domination}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperK-Domination}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Dominationed pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, K-Domination, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Domination alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022),&nbsp; there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperDominating, Neutrosophic SuperHyperDominating theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG162}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Domination alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&#39;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperK-Domination As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperK-Domination In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#168 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). @ResearchGate: https://www.researchgate.net/publication/368752952 &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperK-Number). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperK-Number if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$&nbsp;&nbsp;&nbsp; Neutrosophic re-SuperHyperK-Number if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperK-Number if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$ Neutrosophic rv-SuperHyperK-Number if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number. ((Neutrosophic) SuperHyperK-Number). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; a Neutrosophic SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; an Extreme SuperHyperK-Number SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; a Neutrosophic V-SuperHyperK-Number if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; an Extreme V-SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperK-Number SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperK-Number &nbsp;and Neutrosophic SuperHyperK-Number. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperK-Number is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperK-Number is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperK-Number . Since there&#39;s more ways to get type-results to make a SuperHyperK-Number &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperK-Number, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperK-Number &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperK-Number . It&#39;s redefined a Neutrosophic SuperHyperK-Number &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperK-Number . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperK-Number until the SuperHyperK-Number, then it&#39;s officially called a ``SuperHyperK-Number&#39;&#39; but otherwise, it isn&#39;t a SuperHyperK-Number . There are some instances about the clarifications for the main definition titled a ``SuperHyperK-Number &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperK-Number . For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperK-Number&#39;&#39; and a ``Neutrosophic SuperHyperK-Number &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperK-Number &nbsp;are redefined to a ``Neutrosophic SuperHyperK-Number&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperK-Number &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperK-Number&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperK-Number&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperK-Number &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperK-Number .] SuperHyperK-Number . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperK-Number if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperK-Number &nbsp;or the strongest SuperHyperK-Number &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperK-Number, called SuperHyperK-Number, and the strongest SuperHyperK-Number, called Neutrosophic SuperHyperK-Number, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Number. There isn&#39;t any formation of any SuperHyperK-Number but literarily, it&#39;s the deformation of any SuperHyperK-Number. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperK-Number theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperK-Number, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Number&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperK-Number or the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperK-Number. There isn&#39;t any formation of any SuperHyperK-Number but literarily, it&#39;s the deformation of any SuperHyperK-Number. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperK-Number&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Number&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperK-Number and Neutrosophic&nbsp;&nbsp; SuperHyperK-Number, are figured out in sections ``&nbsp; SuperHyperK-Number&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Number&#39;&#39;. In the sense of tackling on getting results and in K-Number to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperK-Number&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperK-Number&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperK-Number&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Numbered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is an K-Numbered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let an K-Numbered pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperK-Number} if&nbsp; $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperK-Number} if $|E&#39;|=k,~\forall E_a\in E_{NSHG}\setminus E&#39;,~\exists E_b\in E&#39;,\exists V_c\in V,V_c\in E_a,E_b;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperK-Number} if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperK-Number} if $|V&#39;|=k,~\forall V_a\in V_{NSHG}\setminus V&#39;,~\exists V_b\in V&#39;,\exists E_c\in E,V_a,V_b\in V_c ;$&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperK-Number} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperK-Number; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperK-Number SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperK-Number, Neutrosophic re-SuperHyperK-Number, Neutrosophic v-SuperHyperK-Number, and Neutrosophic rv-SuperHyperK-Number and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperK-Number; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperK-Number).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperK-Number} is a Neutrosophic kind of Neutrosophic SuperHyperK-Number such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperK-Number} is a Neutrosophic kind of Neutrosophic SuperHyperK-Number such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperK-Number. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperK-Number more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperK-Number, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperK-Number&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperK-Number. It&#39;s redefined a \textbf{Neutrosophic SuperHyperK-Number} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperK-Number But As The Extensions Excerpt From Dense And Super Forms} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperK-Number. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=2z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperK-Number. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=2z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i\neq2,5}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=4z^3. &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i\neq2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=4z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_3,O\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =5\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \ldots &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_i\}_{i=1}^{10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}=z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=|E_{NSHG}|~\text{choose two}z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=\text{four choose three}z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3,E_4\}. &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z. &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \ldots &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=1}^{|V_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{|V_{NSHG}|}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{22}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^{22}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Quasi-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^{22}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{17}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{17}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{4}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{4}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{3i+1},E_{3j+23}\}_{i,j=0}^3. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{23}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^{23}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_{3i+1},V_{3j+11}\}_{i,j=0}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Quasi-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times3z^8. &nbsp;&nbsp;&nbsp; \\&amp;&amp; \ldots &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^{22}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =6\times5\times3z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^{7}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^{7}. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12},V_{6},V_{8}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =5\times5\times4z^3. &nbsp;\\&amp;&amp; &nbsp;\ldots \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i\}_{i=1}^{14}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =z^{14}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{{E_i}_{i=1}^8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^8. &nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^6. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp; =\{V_i\}_{i\neq 4,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =2\times2\times2\times2\times2z^5. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp; =\{{V_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{{E_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^{10}. &nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=3\times3z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \ldots &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;\\&amp;&amp;=z^6. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}= z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}= 2z^2. &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{V_2,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{22}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^5. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{29}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{29}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^6. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2,V_7,V_{17},V_{27}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =8\times5\times2z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{29}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{29}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{12}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{12}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{{V_{3i+1}}_{{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{11}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{11}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=10z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{10}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{2}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{2}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperK-Number, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^2. &nbsp;\\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{5}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{5}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =5z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;\ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_{3i+1}_{{i=0}}^{\frac{|E_{NSHG}|}{3}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{V^{EXTERNAL}_{3i+1}}_{{i=0}^{\frac{|E_{NSHG}|}{3}}}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=3z^{\frac{|E_{NSHG}|}{3}}. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E_i\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. Then there&#39;s no at least one SuperHyperK-Number. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Number could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Number taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{{E_i}_{E_i\in P_i | |P_i|=\min_{P_j\in E_{NSHG}}|P_j|}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{{V_i}_{V_i\in P_i | |P_i|=\min_{P_j\in V_{NSHG}}|P_j|}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =(|\{P_i~|~|P_i|=\min_{P_j\in E_{NSHG}}|P_j|\}|)z^{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperK-Number taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperK-Number. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperK-Number could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; \ldots &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number}}=\{{E_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperK-Number SuperHyperPolynomial}}=z^{s}. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperK-Number}}=\{{V_i}_{i=1}^{s}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-SuperHyperK-Number SuperHyperPolynomial}}} &nbsp; =z^{s}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperK-Number taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperK-Number. The latter is straightforward. Then there&#39;s at least one SuperHyperK-Number. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperK-Number could be applied. The unique embedded SuperHyperK-Number proposes some longest SuperHyperK-Number excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperK-Number. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperK-Number in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperK-Number,&nbsp; Neutrosophic SuperHyperK-Number, and the Neutrosophic SuperHyperK-Number, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperK-Number is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperK-Number. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperK-Number=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperK-Number of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperK-Number \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperK-Number.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperK-Number and SuperHyperK-Number coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperK-Number if and only if it&#39;s a SuperHyperK-Number. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperK-Number if and only if it&#39;s a longest SuperHyperK-Number. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperK-Number is its SuperHyperK-Number and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperK-Number is its SuperHyperK-Number and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperK-Number isn&#39;t well-defined if and only if its SuperHyperK-Number isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperK-Number is well-defined if and only if its SuperHyperK-Number is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Number/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperK-Number; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperK-Number; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperK-Number/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperK-Number; &nbsp; \item[$(ii):$] the SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperK-Number. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperK-Number; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperK-Number. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperK-Number. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperK-Number/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Number, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperK-Number, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperK-Number set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperK-Number. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperK-Number. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperK-Number; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperK-Number; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperK-Number for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperK-Number for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperK-Number, then $S$ is an s-SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Number, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperK-Number, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperK-Number, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperK-Number. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperK-Number. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperK-Number; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperK-Number. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperK-Number, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number or the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperK-Number} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperK-Number. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperK-Number} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperK-Number. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperK-Number and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperK-Number and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperK-Number and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperK-Number and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperK-Number, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperK-Number. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperK-Number, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperK-Number, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperK-Number and the Neutrosophic&nbsp;&nbsp; SuperHyperK-Number. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperK-Number&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperK-Number}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperK-Number}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an K-Numbered pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, K-Number, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Number alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022),&nbsp; there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperDominating, Neutrosophic SuperHyperDominating theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG162}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)K-Number alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&#39;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperK-Number As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperK-Number In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#183 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). @ResearchGate: https://www.researchgate.net/publication/369087468 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperSpace). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Space pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; Neutrosophic re-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; Neutrosophic rv-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. ((Neutrosophic) SuperHyperSpace). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme SuperHyperSpace SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme V-SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperSpace &nbsp;and Neutrosophic SuperHyperSpace. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperSpace is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperSpace is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperSpace . Since there&#39;s more ways to get type-results to make a SuperHyperSpace &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperSpace . It&#39;s redefined a Neutrosophic SuperHyperSpace &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperSpace . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperSpace until the SuperHyperSpace, then it&#39;s officially called a ``SuperHyperSpace&#39;&#39; but otherwise, it isn&#39;t a SuperHyperSpace . There are some instances about the clarifications for the main definition titled a ``SuperHyperSpace &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperSpace . For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperSpace&#39;&#39; and a ``Neutrosophic SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperSpace &nbsp;are redefined to a ``Neutrosophic SuperHyperSpace&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperSpace &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperSpace&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperSpace&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperSpace &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperSpace .] SuperHyperSpace . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperSpace if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperSpace &nbsp;or the strongest SuperHyperSpace &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperSpace, called SuperHyperSpace, and the strongest SuperHyperSpace, called Neutrosophic SuperHyperSpace, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperSpace theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperSpace, Cancer&#39;s&nbsp; Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath (-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperSpace or the Extreme&nbsp;&nbsp; SuperHyperSpace in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperSpace&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperSpace&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperSpace and Extreme&nbsp;&nbsp; SuperHyperSpace, are figured out in sections ``&nbsp; SuperHyperSpace&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperSpace&#39;&#39;. In the sense of tackling on getting results and in Space to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperSpace&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperSpace&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperSpace&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperSpace. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperSpace more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperSpace&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperSpace. It&#39;s redefined a \textbf{Neutrosophic SuperHyperSpace} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperSpace But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any k-function space like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function space like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. an Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. an Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $m$ and $n$ propose special space. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be an Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability space $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y &minus;3X.$ By linearity of Extreme Expectation, $$E(Z) &ge; E(Y )&minus;3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm&minus;3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form an Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n&minus;1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n&minus;1}in_i.$ Now form an Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability space $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, an Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. an Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be an Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be an Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be an Extreme Variable in a probability space (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n &minus; Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as an Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as an Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_3,V_4,H\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{12},E_{13}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =4z. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^3. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}}= z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; =4z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=6z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}}=12z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =11z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperSpace, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{an Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperSpace in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_j\}_{V^{EXTERNAL}_i\in E_1,V^{EXTERNAL}_j\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{an Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^0. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{an Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperSpace in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{an Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperSpace in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Space}}=\{E^{*}_i,E_1,E_3\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z^{|E^{*}_{NSHG}|+2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; = \{V^{EXTERNAL}_1,V^{EXTERNAL}_3,CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=||E_{NSHG}|z^3. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperSpace taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s at least one SuperHyperSpace. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperSpace could be applied. The unique embedded SuperHyperSpace proposes some longest SuperHyperSpace excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{an Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperSpace in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperSpace,&nbsp; Extreme SuperHyperSpace, and the Extreme SuperHyperSpace, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperSpace is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperSpace. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperSpace=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperSpace of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperSpace \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperSpace.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperSpace and SuperHyperSpace coincide. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is an Extreme SuperHyperSpace if and only if it&#39;s a SuperHyperSpace. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperSpace if and only if it&#39;s a longest SuperHyperSpace. \end{corollary} \begin{corollary} Assume SuperHyperClasses of an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} &nbsp;Assume an Extreme SuperHyperGraph. Then its Extreme SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of an Extreme SuperHyperGraph. Then its Extreme SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume an Extreme SuperHyperGraph. Then its Extreme SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of an Extreme SuperHyperGraph. Then its Extreme SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be an Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperSpace/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperSpace/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperSpace; &nbsp; \item[$(ii):$] the SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperSpace. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperSpace; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperSpace. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is SuperHyperSpace/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperSpace, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperSpace, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperSpace set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperSpace. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperSpace. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperSpace; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperSpace, then $S$ is an s-SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperSpace, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperSpace, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperSpace, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperSpace. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperSpace. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperSpace or the Extreme&nbsp;&nbsp; SuperHyperSpace in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{an Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperSpace} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{an Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperSpace} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperSpace and the Extreme&nbsp;&nbsp; SuperHyperSpace are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperSpace and the Extreme&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperSpace and the Extreme&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperSpace and the Extreme&nbsp;&nbsp; SuperHyperSpace do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperSpace, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperSpace. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperSpace, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperSpace, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperSpace and the Extreme&nbsp;&nbsp; SuperHyperSpace. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperSpace}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperSpace}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme K-Space In SuperHyperGraphs, Neutrosophic K-Space In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). &nbsp; &nbsp; \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Space As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Space In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

Authors: Yeh-Chuin Poh &amp; Ning Wang ### Abstract Mechanical forces are known to play a significant role in biological processes. These forces can be transmitted to the cell through the cytoskeletal filament network, inducing different biochemical responses within the cytoplasm. Although there have been ample reports showing that cytoplasmic enzymes can be directly activated by a local stress on the cell surface via integrins, there has been no evidence that mechanical forces can directly alter nuclear functions without intermediate biochemical cascades. Recently, we showed evidence that forces on the cell membrane can be transmitted directly into the nucleus, inducing structural changes of protein complexes in Cajal bodies. Here, we describe a protocol that utilizes the optical magnetic twisting cytometry (MTC) for force application and fluorescent resonance energy transfer (FRET) to monitor the dynamics and interaction of various Cajal body proteins. ### Introduction It is well known that human bodies are constantly under the influence of mechanical forces. These mechanical forces influence the growth of tissues and organs. Cells integrate both chemical and mechanical cues to regulate biological processes as diverse as differentiation, vascular development, tumor growth and malignancy (1-5). However, little is known about the mechanism by which individual cells sense the mechanical forces and convert them in to biochemical signals within the cell and influence the gene expression, a process known as mechanotransduction. Advances in the field of mechanotransduction have demonstrated that focal adhesion complex proteins such as spectrin (6), talin (7), and integrin (8) can be deformed, unfolded, and thus activated by forces of physiologic magnitudes. Proteins and enzymes within the cytoplasm can be rapidly activated and phosphorylated upon mechanical stress (9, 10). Stem cells differentiate in respond to different surface topology (11), substrate rigidity (12), and applied stress (13), a clear indication of gene expression change within the nucleus. Nonetheless, direct force-altered protein localization/activity and thus gene expression within the nucleus remains elusive. Immunoblotting and immunostaining have been used to study mechanotransduction (14), but these techniques do not provide sufficient resolution and real time results in a single living cell. Because gene expression in a live cell involves many complicated processes in the cytoplasm and the nucleus and takes time, it is impossible, at the present time, to attribute any changes in gene expression to direct effects of the applied force at the cell surface, without involving intermediate biochemical signaling cascades. Therefore, we asked if localizations of protein complexes in the nucleus can be directly altered by a local surface force, since there is evidence that interactions among nuclear proteins are critical in regulating gene expression. We employed a FRET (fluorescence resonance energy transfer) based technique to monitor the dynamics and interaction of proteins within the Cajal Body (CB) complex in response to mechanical stress (15). CBs are critical for the biogenesis and recycling of several classes of small ribonucleoprotein (snRNP) complexes involved in pre-mRNA splicing and preribosomal RNA (pre-rRNA) processing (16, 17), and assembly and delivery of telomerase to telomeres (16-19). Recent advances in the dynamics, assembly, and function of CBs suggest that the CBs organize as a direct reflection of highly active genes with which they are physiologically associated (20). Intermolecular FRET can be used to visualize protein-protein interactions. In this protocol, we labeled various CB proteins with cyan fluorescent protein (CFP) and yellow fluorescent protein (YFP). The CFP labeled protein acts as the donor while the YFP labeled protein act as the receptor. Only CFP is excited during the experiment while both CFP and YFP were monitored simultaneously. By observing the relative intensity changes of CFP and YFP, we can then quantify the distance and interaction between CB proteins. When the CFP and YFP labeled proteins are close to each another (&lt;10nm), FRET occurs when the emission of CFP is transferred to excite YFP. As we observe the FRET ratio of CFP/YFP, there will be a decrease in FRET ratio when the two proteins come closer to each other, because there is a decrease in CFP intensity and an increase in YFP intensity (anti-correlation). On the other hand, when the two proteins are separated and thus there is an increase in distance between the two proteins, the ratio of CFP/YFP will increase. Here, we outline the use of magnetic twisting cytometry (MTC)21 in detail to study the spatial and temporal mechano-chemical response within the cell nucleus. We also describe the use of a dynamic sinusoidal load to quantify the viscoelastic and dissipative behavior between protein pairs within the CB. Our results showed that mechanical force at the apical membrane can be directly transmitted through the actin microfilaments and nuclear envelope to remote cites within the nucleus. The stress induced protein dissociation was rapid and did not require intermediate biochemical signaling, diffusion, or translocation. ### Reagents 1. CFP and YFP plasmid probes of coilin, SMN, fibrillarin, Nopp140, WRAP53, SART3, SmE, SmG (from Miroslav Dundr, Rosalind Franklin University of Medicine and Science, North Chicago) - mCherry-Lamin A plasmid (from Peter Kalab, National Institute of Health) - HeLa cells (ATCC) - Lamin A/C -/- (LMNA-knockout) mouse embryonic fibroblast (from Colin Stewart, - National University of Singapore, Singapore) - Plectin -/- mouse fibroblast (from Gerhard Wiche, University of Vienna, Germany) - CO2-independent medium (Invitrogen) - Collagen, type I from rat tail (solution, Sigma, 091M7675) - Ferromagnetic beads (Fe3O4; 4.5-µm diameter) (from W. Moller, Gauting, Germany or J. Fredberg, Boston, MA; magnetic beads with various surface properties are commercially available in an assortment of sizes from Spherotech, Inc., Lake Forest, IL) - Dimethyl sulfoxide, sterile-filtered (DMSO; Sigma) - Fetal bovine serum (FBS; HyClone) - Opti-MEM I medium (Invitrogen) - Penicillin-streptomycin (Invitrogen) - Phosphate-buffered saline (PBS; HyClone) - L-Glutamine (100x) (Invitrogen) - Lipofectamine 2000 (Invitrogen) - Trolox (6-Hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid; Sigma) - 2% Bis solution (Bio-Rad Laboratories, 161-0142) - 40% Acrylamide solution (Bio-Rad Laboratories, 161-0140) - 3-aminopropyltrimethoxysilane (Aldrich, Product # 281778) - 0.5% gluteraldehyde (Sigma-Aldrich, Product # G6257) - 10% Ammonium persulfate (APS, Bio-Rad) - TEMED (Bio-Rad) - HEPES (Sigma) - Sulfo-SANPAH (Pierce, Product # 22589) - 0.2μm Florescent latex beads (Molecular Probes) - 0.05M Carbonate buffer (pH 9.4; bioWORLD) - Glass-bottomed culture dishes (35-mm diameter; Cell E&G;) - 12 mm circular cover glasses (Fisher, cat. # 12-545-80) - Synthetic RGD-containing peptide [Ac-G(dR)GDSPASSKGGGGS(dR)LLLLLL(dR)-NH2, - Peptide-2000 (Telios) (18); Peptides International, Inc., Louisville, KY] ### Equipment 1. 40×0.55 numerical aperture (N.A.) air and 63×1.32 N.A. oil-immersion objectives (Leica) - CCD camera (Hamamatsu; model C4742-95-12ERG) - CFP/YFP Dual EX/EM (FRET) Filter sets for FRET experiments (Optical Insights): CFP: excitation S430/25, emission S470/30; YFP: excitation S500/20, emission S535/30. The emission filter set uses a 505-nm dichroic mirror. - Dual-View imaging system (Optical Insights) - Inverted microscope (Leica, DMIRE2) - Matlab (Mathworks) - MTC device (Commercially available via special order from EOL Eberhard, Obervil, Switzerland) ### Procedure **Coating magnetic beads with RGD** 1. Suspend the magnetic beads stock in 95% alcohol (for sterilization) and aliquot them into small 2ml vial each containing 1mg of beads. - Leave a vial open and evaporate the alcohol out. - Add 1.5ml of PBS buffer to rinse the beads. Centrifuge it down and discard the PBS carefully. - Add 1ml of Cabonate buffer to the beads. - Add 50 μg of RGD peptides (diluted in DMSO) to the bead-buffer solution. - Rotate the beads at 4OC overnight. - Before using beads, centrifuge the beads and discard the supernatant RGD. Then rinse it once with PBS as described in step 3. - Store the coated beads in serum free DMEM. **Cell culture and transfection** 1. All cells used for experiments are preferred low passages. - Regular cells culture was done in T-25 flask and maintained in DMEM supplemented with 10% FBS100U/ml penicillin, 100μg/ml streptomycin, and 2mM L-Glutamine at 37oC in 5% CO2. - For experiments, cells need to be prepared 3 days in advance. Day 1, coat the 35mm glass bottom dishes with Collagen-I and store at 4oC to allow absorption of collagen on to the glass surface. - Day 2, sterilize the collagen-coated culture dish by leaving it under UV light for 10 minutes. Then seed (~300,000) cells in the collagen-coated 35-mm glass bottom dish such that it is ~80% confluent the following day. - Day 3, double transfect the cells with plasmid constructs of CFP and YFP labeled proteins. Dilute 1μg of CFP plasmid and 1μg of YFP plasmid to 100μg of Opti-MEM I medium in a small vial. - In another vial, add 4μl of Lipofectamine 2000 to 100μg of Opti-MEM I medium in a small vial. - Wait 5 minutes in room temperature before mixing the contents of both vials together. Then wait another 20 minutes. - Add the total ~200μl of DNA-Lipofectamine mixture to the dish containing cells. - Optional: To minimize photobleaching, 0.05mM Trolox solution was added to the dish along with the DNA-Lipofectamine mixture (22). - Incubate for 6 hours at 37oC in 5% CO2 before replacing the culture medium with regular DMEM culture medium. - Day 4, cells are transfected and ready for imaging. **Magnetic Twisting Cytometry (MTC)** 1. On the day of the experiment (day 4 in t in the previous section), take the dish out of the incubator and remove most of the culture medium, such that only the cells in the center well (glass region) is slightly covered in medium. - Add 20μl of RGD-coated magnetic beads (~20μg of beads) to the center well of the dish by scattering them all over. - Carefully place the beads back into the incubator and leave for 10 minutes to allow for integrin clustering and formation of focal adhesions surrounding the beads. - Remove cells from incubator and rinse it once with PBS. Avoid disturbing cells in the center well. Add and remove PBS gently by the side of the dish. - Add CO2-independent medium to the dish. This is to maintain the pH of the cell culture when it is exposed to the open while under the microscope. - Place the dish in the MTC stage where coils are located. Then place it on the inverted microscope. - Find a single cell that is well transfected with both CFP and YFP plasmids. The cell also needs to have a single bead attached to it. Exclude all cells that are not well transfected, have more than one bead attached, or are in contact with neighboring cells. - After the good cell is found, magnetize the magnetic beads by applying a strong magnetic pulse (~1000G, &lt;0.5ms). - Now that the beads are polarized and magnetized, apply a magnetic field in the direction perpendicular to that of the magnetizing pulse. This will cause the bead to rotate. Input the parameter for MTC. Parameters of stress peak magnitude for FRET analysis are typically 17.5Pa (50G step load) or other magnitudes, where for phase lag analysis is 24.5Pa (70G oscillatory load). - While force is being applied, capture the necessary brightfield or fluorescence images. **FRET imaging and analysis** 1. For FRET imaging, the Dual-View imaging system was used to split the image into two (1344×512 pixels each). The top view filters for YFP, while the bottom view filters for CFP. Each image is 1344×1024 pixels and simultaneously captures both CFP and YFP activity. - While force is being applied by the MTC, FRET dual-view time course images are captured to monitor the protein-protein interaction within the nucleus before and after force. - After experiments are done and images obtained. A customized Matlab program is used to analyze the data. The program first divides the top (YFP) and bottom (CFP) image in to two separate files. - The region of interest (an individual CB in our case) is then selected. The program crops this region from the CFP and YFP images, then aligns them by cross-correlation. - A binary mask is then created for CFP and YFP images by using Matlab’s “graythresh” function. The binary mask is then multiplied with the fluorescent images generating images that have only the fluorescing region and a black background. - The CFP/YFP ratio value is then calculated for each individual pixel that has been aligned and cross-correlated. An average of the region is obtained and reported. Each image or time point will generate one CFP/YFP value. - Note: More details on the Matlab program has been described by Na S et. al. (14) **Polyacrylamide gels for traction force measurement** 1. Polyacrylamide (PA) gels with 0.2μm fluorescent beads embedded within are used to measure the traction force each cell generates. By varying the concentration of bis and acrylamide, different gel stiffness can be obtained. - To prepare PA gels, first smear 3-aminopropyltrimethoxysilane over the glass surface of a 35mm glass-bottom-dish using a cotton-tipped swab and let it sit there for 6 min. - Wash it thoroughly with water before applying 100 μl/ dish of 0.5% gluteraldehyde for 30 min. - Wash again thoroughly and let them dry. Avoid touching the glass surface throughout the whole gel making procedure. - Determine the bis:acrylamide solution proportions to get the desired substrate stiffness. 0.6, 2, and 8 kP, corresponds to 0.06% bisacrylamide and 3% acrylamide, 0.05% bisacrylamide and 5% acrylamide, 0.3% bisacrylamide and 5% acrylamide respectively. Prepare 1ml of each desired mixture in a small 2ml vial. - Add 10μl of 0.2μm fluorescent beads to the bis-acrylamide mixture. Before adding fluorescent beads, be sure to vortex or sonicate. - Add polymerizing activator/initiator to the beads-bis-acrylamide mixture. 10% APS at 1: 200 volume ratio (5μl in this case). TEMED at 1: 2000 volume ratio (0.5μl in this case). Mix everything together thoroughly. - Add 15μl of the mixture to the glass surface of the treated dish. (15 μl would give 75 μm thick substrates) - Flatten droplet with a 12mm circular cover glasses. - Turn the glass bottom dish upside down. This ensures the fluorescent beads to be closer to the top surface. - Place the upside down dishes in a 37oC incubator for 30-45 minutes. Elevated temperature helps in the polymerization. - After the gels are fully polymerized, flood the dish with 100 mM HEPES. Then carefully remove the circular cover glass with a single edge razor. - Make 1mM solution of SANPAH with DMSO and 100 mM HEPES. Add DMSO to SANPAH first to dissolve the solid powder, and then add it to HEPES. For example, 5mg SANPAH+50 μl DMSO+ 10 ml (100mM) HEPES. - Take out HEPES from the glass bottom dishes, dab excess HEPES with Kim wipes from around gel edge - Apply 200μl of SANPAH solution the gel (center well of dish). - Expose surface to UV for 6 min (6″ away from the lamp) to photo activate the gel surface. SANPAH color will turn dark. Without SANPAH treatment, collagen will not bind to gel surface. - Rinse off SANPAH with 100mM HEPES. - Repeat photo activation procedure once more and rinse it off with 100mM HEPES. - Coat the gel surface with the desired concentration of collagen and incubate at 4° C overnight. - Before seeding cells onto the gel surface, sterilize it under UV light for 10-15 minutes. - PA gels can be stored in PBS at 4° C for three weeks. - Note: To determine the ratio of bis to acrylamide for desired substrate stiffness, refer to references (23-25). **Traction Force Microscopy (TFM)** 1. Cells are cultured on the PA gels. Depending on the PA gel stiffness, the cell will generate different traction forces, and hence different magnitude of deformation. - Three images need to be captured. First is the brightfield or phase contrast image of the cell which will be used to identify the cell boundary. Second is the fluorescent beads marker image while the cell is still on the substrate. Third is the reference fluorescent beads marker image after the cell has been removed or trypsinized from the gel surface. - A customize Matlab program was used to analyze the traction force generated. The displacement field induced by each individual cell’s tractional forces was determined by comparing the fluorescent bead positions before and after trypsinization (cell-free and thus force-free). - An image correlation method where the flourecent images are divided into small window areas is used to determine the displacement vectors (26). - The root-mean-square (RMS) traction field was then calculated from the displacement field using Fourier Transform Traction Cytometry (FTTC) based on the Boussinesq solution (27). **Cell stiffness measurement** 1. The stress applied to the cell (in Pa) can be calculated from the applied twisting magnetic field (in G) by multiplying the bead constant (in Pa/G) with the applied twisting field (in G). The bead constant reflects the magnetic property of the bead and may differ from batch-to-batch. The beads are calibrated by immersing them in a known viscous fluid, and applying a constant magnetic field while measuring the remnant magnetic field (21). For example, a 50 G applies 17.5 Pa of stress to the cell if the bead constant is 0.35 Pa/G(9). - When a cell with a single bead bound to its apical surface is found under the microscope, an oscillatory stress of 0.3 Hz is applied using the MTC. - The MTC software tracks the displacement coordinates of the magnetic bead and saves them in a text file. - By quantifying the magnetic bead displacement, and the bead embedded area, the cell complex modulus can be estimated. A custom Matlab program is then used to calculate the cell stiffness. - The beads whose displacement waves are synchronized to the input sinusoidal signals were selected. This is to filter out spontaneous movements of the beads or microscope stage shifts. - Beads with displacements less than 5 nm (detectable resolution) and loosely bound beads were not selected for analysis. To increase the signal to noise ratio, the peak amplitude of the displacement was averaged over 5 consecutive cycles for each cell. - The complex stiffness is calculated using the equation G*=T/d. For each bead, the elastic stiffness G’ (the real part of G*) and the dissipative stiffness G” (the imaginary part of G*) was calculated based on the phase lag. The measured stiffness has the units of torque per unit bead volume per unit bead displacement (Pa/nm). - A finite element model is then used to convert the cell stiffness (Pa/nm) to modulus (Pa) based on the bead to cell surface contact (28)(Figure.1).  *Figure 1. Quantification of magnetic bead embedment in HeLa cells. An RGD-coated bead was bound to the apical surface of the cell for ~15 minutes before it was fixed and stained with phalloidin. Integrin-mediated focal adhesions form around the bead-cell contact area, giving rise to an actin ring. The bead embedment was estimated by measuring the actin ring diameter from the fluorescent image and comparing it to the bead diameter from the brightfield image (double arrows). Bead embedment in HeLa cells is 20-30%. Scale bar = 10 μm*. 9.More details on how to calculate cell stiffness have been described by Fabry B et. al. (29). **Phase lag quantification** 1. An oscillatory stress (0.3 Hz or 0.83 Hz) is applied to a cell that is well transfected, similar to the stress used to measure cell stiffness - Time course images of the bead, CFP labeled protein, and YFP labeled protein are captured while the cyclic force is being applied. - A custom Matlab program is used to analyze the images and the displacement of bead, CFP and YFP labeled proteins are determined. The phase lag of fluorescent proteins to the bead is then calculated. - One complete cycle of stress corresponds to 360o. For example, at 0.3 Hz, the period for one complete cycle is 3.33s. If CFP lags behind the bead displacement by 0.3s, that will correspond to a phase lag of ~32o. **Mean Square Displacement (MSD)** 1. For CB dynamics, an oscillatory stress (0.3 Hz) needs to be applied. Fluorescent images used for MSD analysis were obtained using single-view fluorescence filter. - Time course images of the bead, CFP labeled protein, and YFP labeled protein are captured before, during and after the cyclic force is being applied. - Binary images of the bead, CFP and YFP are obtained by using the “graythresh” Matlab function. The centroid coordinates of the bead and each fluorescing protein are then obtained. - The coordinates of each fluorescence particle obtained was then used to calculate the mean square displacement (MSD) of Coilin and SMN. The MSD before, during, and after mechanical loading were calculated using a customized Matlab program based (15). The same procedure is performed on bright-field images to obtain the bead MSD. ### Timing Preparation for experiments takes up to 3 days. Dishes need to be coated with collagen or other matrix proteins. Beads need to be coated with RGD or ligands to integrins. Cells need to be transfected. Depending on the transfection efficiency and how magnetic beads bind to the cell surface, locating an appropriate cell for data collection may take up sometime. The whole process of making PA gels may take a day (excluding incubation time of Collagen-I). ### Troubleshooting Cajal bodies are dynamic and spontaneously move. There are times when the observed CB moves out of focus, especially for those that are not tethered and exhibit simple diffusion. Intermolecular FRET is also difficult to observe because the stoichiometry of acceptors to donors can vary with transfection efficiencies29. On top of that, if the distance or orientations between the protein pairs are unfavorable, FRET may not be observed even if they both reside in the same CB complex. ### Anticipated Results One would expect to observe specific proteins in Cajal bodies that are tethered to chromatin and/or nucleoplasmic filaments to alter localizations or activities in response to a local surface force applied via integrins. ### References 1. Discher, D. E., Janmey, P. &amp; Wang, Y. Tissue Cells Feel and Respond to the Stiffness of their Substrate. *Science* 310, 1139-1143 (2005). - Kumar, S. &amp; Weaver, V. M. Mechanics, malignancy, and metastasis: The force journey of a tumor cell. *Cancer Metastasis Rev*. 28, 113-127 (2009). - Vogel, V. &amp; Sheetz, M. Local force and geometry sensing regulate cell functions. *Nature Reviews Molecular Cell Biology* 7, 265-275 (2006). - Bershadsky, A. D., Balaban, N. Q. &amp; Geiger, B. Adhesion-dependent cell mechanosensitivity. *Annu. Rev. Cell Dev. 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The control of human mesenchymal cell differentiation using nanoscale symmetry and disorder. *Nature Materials* 6, 997-1003 (2007). - Engler, A. J., Sen, S., Sweeney, H. L. &amp; Discher, D. E. Matrix elasticity directs stem cell lineage specification. *Cell* 126, 677-689 (2006). - Chowdhury, F. et al. Material properties of the cell dictate stress-induced spreading and differentiation in embryonic stem cells. *Nat. Mater*. 9, 82-8 (2010). - Na, S. &amp; Wang, N. Application of Fluorescence Resonance Energy Transfer and Magnetic Twisting Cytometry to Quantify Mechanochemical Signaling Activities in a Living Cell. *Science Signaling* 1, pl1 (2008). - Poh YC et al. Dynamic force-induced direct dissociation of protein complexes in a nuclear body in living cells. *Nature Commun*. In press. - Gall, J. G. CAJAL BODIES: The First 100 Years. *Annual Review of Cell &amp; Developmental Biology* 16, 273 (2000). - Sleeman, J. &amp; Lamond, A. Newly assembled snRNPs associate with coiled bodies before speckles, suggesting a nuclear snRNP maturation pathway. *Current Biology* 9, 1065-1074 (1999). - Dundr, M. et al. In vivo kinetics of Cajal body components. *J. Cell Biol*. 164, 831-842 (2004). - Kaiser, T. E., Intine, R. V. &amp; Dundr, M. De Novo Formation of a Subnuclear Body. *Science* 322, 1713-1717 (2008). - Platani, M., Goldberg, I., Lamond, A. I. &amp; Swedlow, J. R. Cajal Body dynamics and association with chromatin are ATP-dependent. *Nat. Cell Biol*. 4, 502 (2002). - Wang, N., Butler, J. P. &amp; Ingber, D. E. Mechanotransduction across the cell surface and through the cytoskeleton. *Science* 260, 1124 (1993). - Rasnik, I., McKinney, S. A. &amp; Ha, T. Nonblinking and long-lasting single-molecule fluorescence imaging. *Nature Methods* 3, 891-893 (2006). - Engler, A. et al. Substrate compliance versus ligand density in cell on gel responses. *Biophys. J*. 86, 617-628 (2004). - Yeung, T. et al. Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. *Cell Motil. Cytoskeleton* 60, 24-34 (2005). - Tse, J. R. &amp; Engler, A. J. Preparation of hydrogel substrates with tunable mechanical properties. *Current protocols in cell biology* / editorial board, Juan S.Bonifacino …[et al.] Chapter 10 (2010). - Tolic-Norrelykke, I. M., Butler, J. P., Chen, J. X. &amp; Wang, N. Spatial and temporal traction response in human airway smooth muscle cells. *American Journal of Physiology-Cell Physiology* 283, C1254-C1266 (2002). - Butler, J. P., Tolic-Norrelykke, I. M., Fabry, B. &amp; Fredberg, J. J. Traction fields, moments, and strain energy that cells exert on their surroundings. *American Journal of Physiology-Cell Physiology* 282, C595-C605 (2002). - Mijailovich, S. M., Kojic, M., Zivkovic, M., Fabry, B. &amp; Fredberg, J. J. A finite element model of cell deformation during magnetic bead twisting. *J. Appl. Physiol*. 93, 1429-1436 (2002). - Fabry, B. et al. Signal transduction in smooth muscle – Selected contribution: Time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells. *J. Appl. Physiol*. 91, 986-994 (2001). - Truong, K. &amp; Ikura, M. The use of FRET imaging microscopy to detect protein-protein interactions and protein conformational changes in vivo. *Curr. Opin. Struct. Biol*. 11, 573-578 (2001). ### Acknowledgements The authors thank Dr. M. Dundr for help and discussion. The work was supported by NIH grant R01 GM072744. ### Associated Publications **Dynamic force-induced direct dissociation of protein complexes in a nuclear body in living cells**. Yeh-Chuin Poh, Sergey P. Shevtsov, Farhan Chowdhury, Douglas C. Wu, Sungsoo Na, Miroslav Dundr, and Ning Wang. *Nature Communications* 3 () 29/05/2012 [doi:10.1038/ncomms1873](http://dx.doi.org/10.1038/ncomms1873) ### Author information **Yeh-Chuin Poh &amp; Ning Wang**, University of Illnois Correspondence to: Ning Wang (nwangrw@illinois.edu) *Source: [Protocol Exchange](http://www.nature.com/protocolexchange/protocols/2357) (2012) doi:10.1038/protex.2012.012. Originally published online 6 June 2012*.

&ldquo;#184 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). @ResearchGate: https://www.researchgate.net/publication/369086888 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperSpace). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Space pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; Neutrosophic re-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp; Neutrosophic rv-SuperHyperSpace if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. ((Neutrosophic) SuperHyperSpace). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme SuperHyperSpace SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; a Neutrosophic V-SuperHyperSpace if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; an Extreme V-SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperSpace SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperSpace &nbsp;and Neutrosophic SuperHyperSpace. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperSpace is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperSpace is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperSpace . Since there&#39;s more ways to get type-results to make a SuperHyperSpace &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperSpace . It&#39;s redefined a Neutrosophic SuperHyperSpace &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperSpace . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperSpace until the SuperHyperSpace, then it&#39;s officially called a ``SuperHyperSpace&#39;&#39; but otherwise, it isn&#39;t a SuperHyperSpace . There are some instances about the clarifications for the main definition titled a ``SuperHyperSpace &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperSpace . For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperSpace&#39;&#39; and a ``Neutrosophic SuperHyperSpace &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperSpace &nbsp;are redefined to a ``Neutrosophic SuperHyperSpace&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperSpace &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperSpace&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperSpace&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperSpace &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperSpace .] SuperHyperSpace . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperSpace if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperSpace &nbsp;or the strongest SuperHyperSpace &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperSpace, called SuperHyperSpace, and the strongest SuperHyperSpace, called Neutrosophic SuperHyperSpace, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperSpace theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperSpace, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperSpace or the Neutrosophic&nbsp;&nbsp; SuperHyperSpace in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperSpace. There isn&#39;t any formation of any SuperHyperSpace but literarily, it&#39;s the deformation of any SuperHyperSpace. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperSpace&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperSpace&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperSpace and Neutrosophic&nbsp;&nbsp; SuperHyperSpace, are figured out in sections ``&nbsp; SuperHyperSpace&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39;. In the sense of tackling on getting results and in Space to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperSpace&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperSpace&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperSpace&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$; \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperSpace} if $S=(V,E)$ is a probability space where $V$ is a sample space and $E$ is a function space $E:V\rightarrow [0,1]$ such that $\sum_{ab\in V}E(ab)=1$;&nbsp;&nbsp; and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperSpace} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperSpace; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperSpace SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperSpace, Neutrosophic re-SuperHyperSpace, Neutrosophic v-SuperHyperSpace, and Neutrosophic rv-SuperHyperSpace and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperSpace; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperSpace).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperSpace} is a Neutrosophic kind of Neutrosophic SuperHyperSpace such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperSpace. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperSpace more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperSpace, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperSpace&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperSpace. It&#39;s redefined a \textbf{Neutrosophic SuperHyperSpace} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperSpace But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Any k-function space like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function space like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $m$ and $n$ propose special space. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability space $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y &minus;3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )&minus;3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm&minus;3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n&minus;1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n&minus;1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability space $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $X_n$ be a Neutrosophic Variable in a probability space (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n &minus; Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability space. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperSpace. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_3,V_4,H\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{12},E_{13}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =4z. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2,E_{13}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_1,V_3,V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^3. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_{12}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^2. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^3. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=6z^3. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}}= z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; =4z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=6z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}}=12z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;&nbsp; \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =11z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperSpace, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-2)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_3\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_j\}_{V^{EXTERNAL}_i\in E_1,V^{EXTERNAL}_j\in E_2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^a. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; =\{CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^0. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i,~E_i\in P_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i,V^{EXTERNAL}_{V^{EXTERNAL}\in P_1\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=(|P^{i}_{NSHG}|\times|P^{j}_{NSHG}|)z^{|P^{\min}_{NSHG}|}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperSpace. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperSpace could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperSpace in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Space}}=\{E^{*}_i,E_1,E_3\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Space SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=|E_{NSHG}|z^{|E^{*}_{NSHG}|+2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Space}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; = \{V^{EXTERNAL}_1,V^{EXTERNAL}_3,CENTER\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Space SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=||E_{NSHG}|z^3. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperSpace taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperSpace. The latter is straightforward. Then there&#39;s at least one SuperHyperSpace. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperSpace could be applied. The unique embedded SuperHyperSpace proposes some longest SuperHyperSpace excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperSpace in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperSpace,&nbsp; Neutrosophic SuperHyperSpace, and the Neutrosophic SuperHyperSpace, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperSpace is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperSpace. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperSpace=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperSpace of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperSpace \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperSpace.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperSpace and SuperHyperSpace coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperSpace if and only if it&#39;s a SuperHyperSpace. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperSpace if and only if it&#39;s a longest SuperHyperSpace. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperSpace is its SuperHyperSpace and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperSpace isn&#39;t well-defined if and only if its SuperHyperSpace isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperSpace is well-defined if and only if its SuperHyperSpace is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperSpace/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperSpace; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperSpace; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperSpace/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperSpace; &nbsp; \item[$(ii):$] the SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperSpace. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperSpace; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperSpace. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperSpace. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperSpace/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperSpace, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperSpace, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperSpace set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperSpace. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperSpace. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperSpace; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperSpace; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperSpace for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperSpace for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperSpace, then $S$ is an s-SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperSpace, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperSpace, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperSpace, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperSpace. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperSpace. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperSpace; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperSpace. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperSpace, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperSpace or the Neutrosophic&nbsp;&nbsp; SuperHyperSpace in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperSpace} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperSpace} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperSpace. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperSpace, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperSpace. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperSpace, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperSpace, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperSpace and the Neutrosophic&nbsp;&nbsp; SuperHyperSpace. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperSpace&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperSpace}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperSpace}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on February 19, 2023. \\ First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It&#39;s first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems&#39;&#39; in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme K-Space In SuperHyperGraphs, Neutrosophic K-Space In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413).&nbsp; (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf).&nbsp; (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34). \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). &nbsp; &nbsp; \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Space As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Space In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). &nbsp; \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). &nbsp; \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). &nbsp; \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). &nbsp; \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). &nbsp; &nbsp; &nbsp; &nbsp; \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#192 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Nebulizer By Hyper Nub Of Clique-Neighbors In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29764.71046). @ResearchGate: https://www.researchgate.net/publication/369196478 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Nebulizer By Hyper Nub Of Clique-Neighbors In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Neighbors). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Neighbors pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Neighbors if the following expression is called Neutrosophic e-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} &nbsp;Neutrosophic re-SuperHyperClique-Neighbors if the following expression is called Neutrosophic e-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Neighbors&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Neighbors if the following expression is called Neutrosophic v-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors. ((Neutrosophic) SuperHyperClique-Neighbors). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; a Neutrosophic SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; an Extreme SuperHyperClique-Neighbors SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; a Neutrosophic V-SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; an Extreme V-SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Neighbors &nbsp;and Neutrosophic SuperHyperClique-Neighbors. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Neighbors is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Neighbors is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Neighbors . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Neighbors &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Neighbors &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Neighbors . It&#39;s redefined a Neutrosophic SuperHyperClique-Neighbors &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Neighbors . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Neighbors until the SuperHyperClique-Neighbors, then it&#39;s officially called a ``SuperHyperClique-Neighbors&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Neighbors . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Neighbors &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Neighbors . For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; and a ``Neutrosophic SuperHyperClique-Neighbors &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Neighbors &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Neighbors &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Neighbors &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Neighbors .] SuperHyperClique-Neighbors . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Neighbors if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Neighbors &nbsp;or the strongest SuperHyperClique-Neighbors &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Neighbors, called SuperHyperClique-Neighbors, and the strongest SuperHyperClique-Neighbors, called Neutrosophic SuperHyperClique-Neighbors, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Neighbors. There isn&#39;t any formation of any SuperHyperClique-Neighbors but literarily, it&#39;s the deformation of any SuperHyperClique-Neighbors. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Neighbors theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperClique-Neighbors, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Neighbors or the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Neighbors. There isn&#39;t any formation of any SuperHyperClique-Neighbors but literarily, it&#39;s the deformation of any SuperHyperClique-Neighbors. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Neighbors and Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors, are figured out in sections ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39;. In the sense of tackling on getting results and in Clique-Neighbors to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Neighbors&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Neighbors&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Neighbors of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Neighbors of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Neighbors} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Neighbors} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Neighbors such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Neighbors} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Neighbors such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Neighbors. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Neighbors more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Neighbors. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Neighbors} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperClique-Neighbors But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Any k-function Clique-Neighbors like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function Clique-Neighbors like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $m$ and $n$ propose special Clique-Neighbors. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability Clique-Neighbors $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Extreme Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Neighbors $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X_n$ be a Extreme Variable in a probability Clique-Neighbors (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Neighbors. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Neighbors. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}=\{V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_6,V_{15},V_9,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5_2z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,\ldots\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,\ldots\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =az. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_2,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =0z^0. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{i_{i=1,2,3}},V_{j_{j=4,5,6,7}},V_{k_{k=8,9,10,11}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =0z^0. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^{10}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_{i_{{i=1}^7}},V_{j{{j=8}^{11}}},V_{k{{k=1}^3}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=0z^0. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}=\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=2,3,4,5,6}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{E_i\}_{i=4,5,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=0z^0. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}=\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}}=\{V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}}= 2z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; =0z^0. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}},V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+z^5+z^4+z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=23}^{29}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+z^6+z^5+z^4. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=24}^{29}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+2z^5+z^4. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_{i_{V_i\in E_8,~i\neq7,8}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =az^{6}+\ldots+z^3. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =az^b+\ldots+cz^b. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z^9. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Neighbors, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{H_6,O_6,E_6,C_6,\ldots,\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^{11}+4z^9+5z^8+4z^5. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Neighbors minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Neighbors, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Neighbors is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Neighbors is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Neighbors in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Neighbors. \end{proposition} \begin{proposition} &nbsp;Assume a simple Extreme SuperHyperGraph $ESHG:(V,E).$ Then the Extreme number of&nbsp; type-result-R-Clique-Neighbors has, the least Extreme cardinality, the lower sharp Extreme bound for Extreme cardinality, is the Extreme cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Extreme type-result-R-Clique-Neighbors with the least Extreme cardinality, the lower sharp Extreme bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Extreme type-result-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme type-result-Clique-Neighbors is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Neighbors since neither amount of Extreme SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Extreme number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Extreme SuperHyperSet of the Extreme SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices but the maximum Extreme cardinality indicates that these Extreme&nbsp; type-SuperHyperSets couldn&#39;t give us the Extreme lower bound in the term of Extreme sharpness. In other words, the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Extreme SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Extreme SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Extreme SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Neighbors is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Extreme SuperHyperClasses of the connected loopless Extreme SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Neighbors. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Extreme SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Extreme structure of the Extreme R-Clique-Neighbors decorates the Extreme SuperHyperVertices don&#39;t have received any Extreme connections so as this Extreme style implies different versions of Extreme SuperHyperEdges with the maximum Extreme cardinality in the terms of Extreme SuperHyperVertices are spotlight. The lower Extreme bound is to have the maximum Extreme groups of Extreme SuperHyperVertices have perfect Extreme connections inside each of SuperHyperEdges and the outside of this Extreme SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Extreme SuperHyperGraph arising from its Extreme properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Extreme SuperHyperVertex in the targeted Extreme SuperHyperSet, then there&#39;s no Extreme connection. Furthermore, the Extreme existence of one Extreme SuperHyperVertex has no&nbsp; Extreme effect to talk about the Extreme R-Clique-Neighbors. Since at least two Extreme SuperHyperVertices involve to make a title in the Extreme background of the Extreme SuperHyperGraph. The Extreme SuperHyperGraph is obvious if it has no Extreme SuperHyperEdge but at least two Extreme SuperHyperVertices make the Extreme version of Extreme SuperHyperEdge. Thus in the Extreme setting of non-obvious Extreme SuperHyperGraph, there are at least one Extreme SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Extreme adjective for the initial Extreme SuperHyperGraph, induces there&#39;s no Extreme&nbsp; appearance of the loop Extreme version of the Extreme SuperHyperEdge and this Extreme SuperHyperGraph is said to be loopless. The Extreme adjective ``loop&#39;&#39; on the basic Extreme framework engages one Extreme SuperHyperVertex but it never happens in this Extreme setting. With these Extreme bases, on a Extreme SuperHyperGraph, there&#39;s at least one Extreme SuperHyperEdge thus there&#39;s at least a Extreme R-Clique-Neighbors has the Extreme cardinality of a Extreme SuperHyperEdge. Thus, a Extreme R-Clique-Neighbors has the Extreme cardinality at least a Extreme SuperHyperEdge. Assume a Extreme SuperHyperSet $V\setminus V\setminus \{z\}.$ This Extreme SuperHyperSet isn&#39;t a Extreme R-Clique-Neighbors since either the Extreme SuperHyperGraph is an obvious Extreme SuperHyperModel thus it never happens since there&#39;s no Extreme usage of this Extreme framework and even more there&#39;s no Extreme connection inside or the Extreme SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Extreme contradiction with the term ``Extreme R-Clique-Neighbors&#39;&#39; since the maximum Extreme cardinality never happens for this Extreme style of the Extreme SuperHyperSet and beyond that there&#39;s no Extreme connection inside as mentioned in first Extreme case in the forms of drawback for this selected Extreme SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Extreme case implies having the Extreme style of on-quasi-triangle Extreme style on the every Extreme elements of this Extreme SuperHyperSet. Precisely, the Extreme R-Clique-Neighbors is the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that some Extreme amount of the Extreme SuperHyperVertices are on-quasi-triangle Extreme style. The Extreme cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Extreme bound is up. Thus the minimum Extreme cardinality of the maximum Extreme cardinality ends up the Extreme discussion. The first Extreme term refers to the Extreme setting of the Extreme SuperHyperGraph but this key point is enough since there&#39;s a Extreme SuperHyperClass of a Extreme SuperHyperGraph has no on-quasi-triangle Extreme style amid some amount of its Extreme SuperHyperVertices. This Extreme setting of the Extreme SuperHyperModel proposes a Extreme SuperHyperSet has only some amount&nbsp; Extreme SuperHyperVertices from one Extreme SuperHyperEdge such that there&#39;s no Extreme amount of Extreme SuperHyperEdges more than one involving these some amount of these Extreme SuperHyperVertices. The Extreme cardinality of this Extreme SuperHyperSet is the maximum and the Extreme case is occurred in the minimum Extreme situation. To sum them up, the Extreme SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Extreme cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Extreme SuperHyperVertices such that there&#39;s distinct-covers-order-amount Extreme SuperHyperEdges for amount of Extreme SuperHyperVertices taken from the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Extreme SuperHyperSet of the Extreme SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Extreme&nbsp; R-Clique-Neighbors for the Extreme SuperHyperGraph as used Extreme background in the Extreme terms of worst Extreme case and the common theme of the lower Extreme bound occurred in the specific Extreme SuperHyperClasses of the Extreme SuperHyperGraphs which are Extreme free-quasi-triangle. &nbsp; \\ Assume a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Extreme number of the Extreme SuperHyperVertices. Then every Extreme SuperHyperVertex has at least no Extreme SuperHyperEdge with others in common. Thus those Extreme SuperHyperVertices have the eligibles to be contained in a Extreme R-Clique-Neighbors. Those Extreme SuperHyperVertices are potentially included in a Extreme&nbsp; style-R-Clique-Neighbors. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Extreme SuperHyperVertices of a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Extreme&nbsp; SuperHyperVertices of the Extreme SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices and there&#39;s only and only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Extreme SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Extreme R-Clique-Neighbors is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Extreme R-Clique-Neighbors but with slightly differences in the maximum Extreme cardinality amid those Extreme type-SuperHyperSets of the Extreme SuperHyperVertices. Thus the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Extreme cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Extreme R-Clique-Neighbors. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices belong to the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Neighbors}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Neighbors}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Extreme quasi-R-Clique-Neighbors where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Extreme intended SuperHyperVertices but in a Extreme Clique-Neighbors, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Neighbors is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Neighbors is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Neighbors in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Neighbors. \\ The obvious SuperHyperGraph has no Extreme SuperHyperEdges. But the non-obvious Extreme SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Extreme optimal SuperHyperObject. It specially delivers some remarks on the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that there&#39;s distinct amount of Extreme SuperHyperEdges for distinct amount of Extreme SuperHyperVertices up to all&nbsp; taken from that Extreme SuperHyperSet of the Extreme SuperHyperVertices but this Extreme SuperHyperSet of the Extreme SuperHyperVertices is either has the maximum Extreme SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Extreme SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Extreme SuperHyperEdge containing at least all Extreme SuperHyperVertices. Thus it forms a Extreme quasi-R-Clique-Neighbors where the Extreme completion of the Extreme incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Extreme embedded R-Clique-Neighbors. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Extreme SuperHyperCardinality and they&#39;re Extreme SuperHyperOptimal. The less than two distinct types of Extreme SuperHyperVertices are included in the minimum Extreme style of the embedded Extreme R-Clique-Neighbors. The interior types of the Extreme SuperHyperVertices are deciders. Since the Extreme number of SuperHyperNeighbors are only&nbsp; affected by the interior Extreme SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Extreme SuperHyperSet for any distinct types of Extreme SuperHyperVertices pose the Extreme R-Clique-Neighbors. Thus Extreme exterior SuperHyperVertices could be used only in one Extreme SuperHyperEdge and in Extreme SuperHyperRelation with the interior Extreme SuperHyperVertices in that&nbsp; Extreme SuperHyperEdge. In the embedded Extreme Clique-Neighbors, there&#39;s the usage of exterior Extreme SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Extreme SuperHyperVertex has no connection, inside. Thus, the Extreme SuperHyperSet of the Extreme SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Extreme R-Clique-Neighbors. The Extreme R-Clique-Neighbors with the exclusion of the exclusion of all&nbsp; Extreme SuperHyperVertices in one Extreme SuperHyperEdge and with other terms, the Extreme R-Clique-Neighbors with the inclusion of all Extreme SuperHyperVertices in one Extreme SuperHyperEdge, is a Extreme quasi-R-Clique-Neighbors. To sum them up, in a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Neighbors minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Neighbors, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Extreme R-Clique-Neighbors has two titles. a Extreme quasi-R-Clique-Neighbors and its corresponded quasi-maximum Extreme R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Extreme number, there&#39;s a Extreme quasi-R-Clique-Neighbors with that quasi-maximum Extreme SuperHyperCardinality in the terms of the embedded Extreme SuperHyperGraph. If there&#39;s an embedded Extreme SuperHyperGraph, then the Extreme quasi-SuperHyperNotions lead us to take the collection of all the Extreme quasi-R-Clique-Neighborss for all Extreme numbers less than its Extreme corresponded maximum number. The essence of the Extreme Clique-Neighbors ends up but this essence starts up in the terms of the Extreme quasi-R-Clique-Neighbors, again and more in the operations of collecting all the Extreme quasi-R-Clique-Neighborss acted on the all possible used formations of the Extreme SuperHyperGraph to achieve one Extreme number. This Extreme number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Neighborss. Let $z_{\text{Extreme Number}},S_{\text{Extreme SuperHyperSet}}$ and $G_{\text{Extreme Clique-Neighbors}}$ be a Extreme number, a Extreme SuperHyperSet and a Extreme Clique-Neighbors. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Extreme Number}}]_{\text{Extreme Class}}=\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Extreme Clique-Neighbors is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Extreme Clique-Neighbors. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Extreme Clique-Neighbors poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Extreme SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Extreme SuperHyperVertices such that any amount of its Extreme SuperHyperVertices are incident to a Extreme&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Extreme&nbsp; Quasi-Clique-Neighbors&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Extreme&nbsp; Quasi-Clique-Neighbors&#39;&#39; since ``Extreme Quasi-Clique-Neighbors&#39;&#39; happens ``Extreme Clique-Neighbors&#39;&#39; in a Extreme SuperHyperGraph as initial framework and background but ``Extreme SuperHyperNeighborhood&#39;&#39; may not happens ``Extreme Clique-Neighbors&#39;&#39; in a Extreme SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Extreme SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Extreme SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Extreme Quasi-Clique-Neighbors&#39;&#39;, and&nbsp; ``Extreme Clique-Neighbors&#39;&#39; are up. \\ Thus, let $z_{\text{Extreme Number}},N_{\text{Extreme SuperHyperNeighborhood}}$ and $G_{\text{Extreme Clique-Neighbors}}$ be a Extreme number, a Extreme SuperHyperNeighborhood and a Extreme Clique-Neighbors and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperVertices is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Neighbors. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Extreme SuperHyperSet of Extreme SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Neighbors. The Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Extreme R-Clique-Neighbors}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge amid some Extreme SuperHyperVertices instead of all given by \underline{\textbf{Extreme Clique-Neighbors}} is related to the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Extreme SuperHyperVertex \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Neighbors is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Neighbors is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Extreme SuperHyperVertex. But the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Neighbors \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Neighbors. Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Extreme R-Clique-Neighbors $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Neighbors \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Neighbors}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme SuperHyperEdge for some amount Extreme&nbsp; SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Neighbors. There isn&#39;t&nbsp; only less than two Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Extreme R-Clique-Neighbors, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Neighbors, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Extreme SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; R-Clique-Neighbors&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme R-Clique-Neighbors}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Extreme SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Extreme free-triangle embedded SuperHyperModel and a Extreme on-triangle embedded SuperHyperModel but also it&#39;s a Extreme stable embedded SuperHyperModel. But all only non-obvious simple Extreme type-SuperHyperSets of the Extreme&nbsp; R-Clique-Neighbors amid those obvious simple Extreme type-SuperHyperSets of the Extreme Clique-Neighbors, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Extreme R-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme&nbsp; R-Clique-Neighbors is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Extreme SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Extreme SuperHyperVertices $r.$ Consider all Extreme numbers of those Extreme SuperHyperVertices from that Extreme SuperHyperEdge excluding excluding more than $r$ distinct Extreme SuperHyperVertices, exclude to any given Extreme SuperHyperSet of the Extreme SuperHyperVertices. Consider there&#39;s a Extreme&nbsp; R-Clique-Neighbors with the least cardinality, the lower sharp Extreme bound for Extreme cardinality. Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The Extreme SuperHyperSet of the Extreme SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Extreme SuperHyperSet $S$ of&nbsp; the Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have&nbsp; some Extreme SuperHyperVertices uniquely but it isn&#39;t a Extreme R-Clique-Neighbors. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have some SuperHyperVertices uniquely. The Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Extreme cardinality of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices but it isn&#39;t a Extreme R-Clique-Neighbors. Since it \textbf{\underline{doesn&#39;t do}} the Extreme procedure such that such that there&#39;s a Extreme SuperHyperEdge to have some Extreme&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Extreme SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Extreme SuperHyperGraph $ESHG:(V,E),$ a Extreme SuperHyperVertex, titled its Extreme SuperHyperNeighbor,&nbsp; to that Extreme SuperHyperVertex in the Extreme SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Extreme procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Extreme SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Extreme SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Extreme SuperHyperNeighborhood. Thus the obvious Extreme R-Clique-Neighbors,&nbsp; $V_{ESHE}$ is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Neighbors,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Extreme SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Extreme SuperHyperVertices does forms any kind of Extreme pairs are titled&nbsp;&nbsp; \underline{Extreme SuperHyperNeighbors} in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Extreme SuperHyperCardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Extreme SuperHyperEdge to have some Extreme SuperHyperVertices uniquely. Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Any Extreme R-Clique-Neighbors only contains all interior Extreme SuperHyperVertices and all exterior Extreme SuperHyperVertices from the unique Extreme SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Extreme SuperHyperNeighbors in and there&#39;s all&nbsp; Extreme SuperHyperNeighborhoods in with no exception minus all&nbsp; Extreme SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Extreme SuperHyperNeighborhoods and Extreme SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Neighbors, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Extreme type-SuperHyperSet of the Extreme Clique-Neighbors. &nbsp;The Extreme SuperHyperSet of Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Extreme type-SuperHyperSet of the Extreme Clique-Neighbors. The Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Extreme Clique-Neighbors}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Extreme SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Neighbors is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Neighbors is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Extreme SuperHyperVertices. But the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Neighbors \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Neighbors. Since the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Extreme Clique-Neighbors $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Neighbors \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Neighbors}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There aren&#39;t&nbsp; only less than three Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Extreme Clique-Neighbors, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Neighbors, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Extreme SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; Clique-Neighbors&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme Clique-Neighbors}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Neighbors. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Neighbors taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Neighbors taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Neighbors. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Neighbors taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Neighbors. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. The unique embedded SuperHyperClique-Neighbors proposes some longest SuperHyperClique-Neighbors excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Neighbors in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Neighbors,&nbsp; Extreme SuperHyperClique-Neighbors, and the Extreme SuperHyperClique-Neighbors, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperClique-Neighbors is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperClique-Neighbors. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperClique-Neighbors=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Neighbors of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Neighbors \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperClique-Neighbors.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperClique-Neighbors and SuperHyperClique-Neighbors coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperClique-Neighbors if and only if it&#39;s a SuperHyperClique-Neighbors. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Neighbors if and only if it&#39;s a longest SuperHyperClique-Neighbors. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Neighbors is its SuperHyperClique-Neighbors and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Neighbors is its SuperHyperClique-Neighbors and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Neighbors/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Neighbors/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] the SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperClique-Neighbors/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Neighbors set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Neighbors. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Neighbors. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Neighbors. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Neighbors. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors or the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Neighbors} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperClique-Neighbors. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Neighbors} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperClique-Neighbors. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Neighbors and the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Neighbors and the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Neighbors and the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Neighbors and the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Neighbors, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Neighbors. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Neighbors, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Neighbors and the Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Neighbors}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperClique-Neighbors}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#185 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Lith By Hyper Lite Of List-Coloring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.16356.04489). @ResearchGate: https://www.researchgate.net/publication/369113233 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Lith By Hyper Lite Of List-Coloring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperList-Coloring). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a List-Coloring pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperList-Coloring if the following expression is called Neutrosophic e-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*}&nbsp; Neutrosophic re-SuperHyperList-Coloring if the following expression is called Neutrosophic e-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperList-Coloring&nbsp; if the following expression is called Neutrosophic v-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperList-Coloring if the following expression is called Neutrosophic v-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring. ((Neutrosophic) SuperHyperList-Coloring). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; a Neutrosophic SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; an Extreme SuperHyperList-Coloring SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; a Neutrosophic V-SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; an Extreme V-SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperList-Coloring &nbsp;and Neutrosophic SuperHyperList-Coloring. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperList-Coloring is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperList-Coloring is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperList-Coloring . Since there&#39;s more ways to get type-results to make a SuperHyperList-Coloring &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperList-Coloring &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperList-Coloring . It&#39;s redefined a Neutrosophic SuperHyperList-Coloring &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperList-Coloring . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperList-Coloring until the SuperHyperList-Coloring, then it&#39;s officially called a ``SuperHyperList-Coloring&#39;&#39; but otherwise, it isn&#39;t a SuperHyperList-Coloring . There are some instances about the clarifications for the main definition titled a ``SuperHyperList-Coloring &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperList-Coloring . For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; and a ``Neutrosophic SuperHyperList-Coloring &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperList-Coloring &nbsp;are redefined to a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperList-Coloring &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperList-Coloring&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperList-Coloring &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperList-Coloring .] SuperHyperList-Coloring . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperList-Coloring if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperList-Coloring &nbsp;or the strongest SuperHyperList-Coloring &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperList-Coloring, called SuperHyperList-Coloring, and the strongest SuperHyperList-Coloring, called Neutrosophic SuperHyperList-Coloring, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperList-Coloring. There isn&#39;t any formation of any SuperHyperList-Coloring but literarily, it&#39;s the deformation of any SuperHyperList-Coloring. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperList-Coloring theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperList-Coloring, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperList-Coloring&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath (-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperList-Coloring or the Extreme&nbsp;&nbsp; SuperHyperList-Coloring in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperList-Coloring. There isn&#39;t any formation of any SuperHyperList-Coloring but literarily, it&#39;s the deformation of any SuperHyperList-Coloring. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperList-Coloring&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperList-Coloring and Extreme&nbsp;&nbsp; SuperHyperList-Coloring, are figured out in sections ``&nbsp; SuperHyperList-Coloring&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39;. In the sense of tackling on getting results and in List-Coloring to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperList-Coloring&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperList-Coloring&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a List-Coloring of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a List-Coloring of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic e-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic re-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic v-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperList-Coloring} f the following expression is called \textbf{Neutrosophic v-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperList-Coloring} is a Neutrosophic kind of Neutrosophic SuperHyperList-Coloring such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperList-Coloring} is a Neutrosophic kind of Neutrosophic SuperHyperList-Coloring such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperList-Coloring. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperList-Coloring more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperList-Coloring&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperList-Coloring. It&#39;s redefined a \textbf{Neutrosophic SuperHyperList-Coloring} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperList-Coloring But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Any k-function List-Coloring like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function List-Coloring like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. an Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. an Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $m$ and $n$ propose special List-Coloring. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be an Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability List-Coloring $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Extreme Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form an Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form an Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability List-Coloring $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, an Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. an Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be an Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be an Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X_n$ be an Extreme Variable in a probability List-Coloring (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as an Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as an Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperList-Coloring. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperList-Coloring. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=2z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_1,V_2,V_3,N,F\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =(\text{Seven Choose Four})z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=4z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i,V_{13}\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{13},V_i\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =2z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_i,V_{13}\}_{i=1}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=5z^2. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=z^5. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=6z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}}= 2z^3. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; =2z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}}=11z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{V_i\in E_2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z^{7}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{10}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_i\}_{V_i\in E_6}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10z^{|E_6|}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperList-Coloring, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{M_6,L_6,F,V_3,V_2,H_6,O_6,E_6,C_6,Z_5,W_5,V_{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{12}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-List-Coloring if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-List-Coloring minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-List-Coloring, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If an Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-List-Coloring is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-List-Coloring is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme List-Coloring in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in an Extreme R-List-Coloring. \end{proposition} \begin{proposition} &nbsp;Assume a simple Extreme SuperHyperGraph $ESHG:(V,E).$ Then the Extreme number of&nbsp; type-result-R-List-Coloring has, the least Extreme cardinality, the lower sharp Extreme bound for Extreme cardinality, is the Extreme cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s an Extreme type-result-R-List-Coloring with the least Extreme cardinality, the lower sharp Extreme bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=z^5. \end{eqnarray*} Is an Extreme type-result-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of an Extreme type-result-List-Coloring is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-List-Coloring since neither amount of Extreme SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Extreme number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Extreme SuperHyperSet of the Extreme SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Extreme SuperHyperVertex of an Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices but the maximum Extreme cardinality indicates that these Extreme&nbsp; type-SuperHyperSets couldn&#39;t give us the Extreme lower bound in the term of Extreme sharpness. In other words, the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Extreme SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Extreme SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Extreme SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-List-Coloring is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Extreme SuperHyperClasses of the connected loopless Extreme SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-List-Coloring. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Extreme SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Extreme structure of the Extreme R-List-Coloring decorates the Extreme SuperHyperVertices don&#39;t have received any Extreme connections so as this Extreme style implies different versions of Extreme SuperHyperEdges with the maximum Extreme cardinality in the terms of Extreme SuperHyperVertices are spotlight. The lower Extreme bound is to have the maximum Extreme groups of Extreme SuperHyperVertices have perfect Extreme connections inside each of SuperHyperEdges and the outside of this Extreme SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Extreme SuperHyperGraph arising from its Extreme properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Extreme SuperHyperVertex in the targeted Extreme SuperHyperSet, then there&#39;s no Extreme connection. Furthermore, the Extreme existence of one Extreme SuperHyperVertex has no&nbsp; Extreme effect to talk about the Extreme R-List-Coloring. Since at least two Extreme SuperHyperVertices involve to make a title in the Extreme background of the Extreme SuperHyperGraph. The Extreme SuperHyperGraph is obvious if it has no Extreme SuperHyperEdge but at least two Extreme SuperHyperVertices make the Extreme version of Extreme SuperHyperEdge. Thus in the Extreme setting of non-obvious Extreme SuperHyperGraph, there are at least one Extreme SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Extreme adjective for the initial Extreme SuperHyperGraph, induces there&#39;s no Extreme&nbsp; appearance of the loop Extreme version of the Extreme SuperHyperEdge and this Extreme SuperHyperGraph is said to be loopless. The Extreme adjective ``loop&#39;&#39; on the basic Extreme framework engages one Extreme SuperHyperVertex but it never happens in this Extreme setting. With these Extreme bases, on an Extreme SuperHyperGraph, there&#39;s at least one Extreme SuperHyperEdge thus there&#39;s at least an Extreme R-List-Coloring has the Extreme cardinality of an Extreme SuperHyperEdge. Thus, an Extreme R-List-Coloring has the Extreme cardinality at least an Extreme SuperHyperEdge. Assume an Extreme SuperHyperSet $V\setminus V\setminus \{z\}.$ This Extreme SuperHyperSet isn&#39;t an Extreme R-List-Coloring since either the Extreme SuperHyperGraph is an obvious Extreme SuperHyperModel thus it never happens since there&#39;s no Extreme usage of this Extreme framework and even more there&#39;s no Extreme connection inside or the Extreme SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s an Extreme contradiction with the term ``Extreme R-List-Coloring&#39;&#39; since the maximum Extreme cardinality never happens for this Extreme style of the Extreme SuperHyperSet and beyond that there&#39;s no Extreme connection inside as mentioned in first Extreme case in the forms of drawback for this selected Extreme SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Extreme case implies having the Extreme style of on-quasi-triangle Extreme style on the every Extreme elements of this Extreme SuperHyperSet. Precisely, the Extreme R-List-Coloring is the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that some Extreme amount of the Extreme SuperHyperVertices are on-quasi-triangle Extreme style. The Extreme cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Extreme bound is up. Thus the minimum Extreme cardinality of the maximum Extreme cardinality ends up the Extreme discussion. The first Extreme term refers to the Extreme setting of the Extreme SuperHyperGraph but this key point is enough since there&#39;s an Extreme SuperHyperClass of an Extreme SuperHyperGraph has no on-quasi-triangle Extreme style amid some amount of its Extreme SuperHyperVertices. This Extreme setting of the Extreme SuperHyperModel proposes an Extreme SuperHyperSet has only some amount&nbsp; Extreme SuperHyperVertices from one Extreme SuperHyperEdge such that there&#39;s no Extreme amount of Extreme SuperHyperEdges more than one involving these some amount of these Extreme SuperHyperVertices. The Extreme cardinality of this Extreme SuperHyperSet is the maximum and the Extreme case is occurred in the minimum Extreme situation. To sum them up, the Extreme SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Extreme cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Extreme SuperHyperVertices such that there&#39;s distinct-covers-order-amount Extreme SuperHyperEdges for amount of Extreme SuperHyperVertices taken from the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Extreme SuperHyperSet of the Extreme SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an Extreme&nbsp; R-List-Coloring for the Extreme SuperHyperGraph as used Extreme background in the Extreme terms of worst Extreme case and the common theme of the lower Extreme bound occurred in the specific Extreme SuperHyperClasses of the Extreme SuperHyperGraphs which are Extreme free-quasi-triangle. &nbsp; \\ Assume an Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Extreme number of the Extreme SuperHyperVertices. Then every Extreme SuperHyperVertex has at least no Extreme SuperHyperEdge with others in common. Thus those Extreme SuperHyperVertices have the eligibles to be contained in an Extreme R-List-Coloring. Those Extreme SuperHyperVertices are potentially included in an Extreme&nbsp; style-R-List-Coloring. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Extreme SuperHyperVertices of an Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Extreme&nbsp; SuperHyperVertices of the Extreme SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices and there&#39;s only and only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Extreme SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Extreme R-List-Coloring is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Extreme R-List-Coloring but with slightly differences in the maximum Extreme cardinality amid those Extreme type-SuperHyperSets of the Extreme SuperHyperVertices. Thus the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Extreme cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Extreme R-List-Coloring. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices belong to the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-List-Coloring}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-List-Coloring}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is an Extreme quasi-R-List-Coloring where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Extreme intended SuperHyperVertices but in an Extreme List-Coloring, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If an Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-List-Coloring is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-List-Coloring is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme List-Coloring in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in an Extreme R-List-Coloring. \\ The obvious SuperHyperGraph has no Extreme SuperHyperEdges. But the non-obvious Extreme SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Extreme optimal SuperHyperObject. It specially delivers some remarks on the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that there&#39;s distinct amount of Extreme SuperHyperEdges for distinct amount of Extreme SuperHyperVertices up to all&nbsp; taken from that Extreme SuperHyperSet of the Extreme SuperHyperVertices but this Extreme SuperHyperSet of the Extreme SuperHyperVertices is either has the maximum Extreme SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Extreme SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Extreme SuperHyperEdge containing at least all Extreme SuperHyperVertices. Thus it forms an Extreme quasi-R-List-Coloring where the Extreme completion of the Extreme incidence is up in that.&nbsp; Thus it&#39;s, literarily, an Extreme embedded R-List-Coloring. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Extreme SuperHyperCardinality and they&#39;re Extreme SuperHyperOptimal. The less than two distinct types of Extreme SuperHyperVertices are included in the minimum Extreme style of the embedded Extreme R-List-Coloring. The interior types of the Extreme SuperHyperVertices are deciders. Since the Extreme number of SuperHyperNeighbors are only&nbsp; affected by the interior Extreme SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Extreme SuperHyperSet for any distinct types of Extreme SuperHyperVertices pose the Extreme R-List-Coloring. Thus Extreme exterior SuperHyperVertices could be used only in one Extreme SuperHyperEdge and in Extreme SuperHyperRelation with the interior Extreme SuperHyperVertices in that&nbsp; Extreme SuperHyperEdge. In the embedded Extreme List-Coloring, there&#39;s the usage of exterior Extreme SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Extreme SuperHyperVertex has no connection, inside. Thus, the Extreme SuperHyperSet of the Extreme SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Extreme R-List-Coloring. The Extreme R-List-Coloring with the exclusion of the exclusion of all&nbsp; Extreme SuperHyperVertices in one Extreme SuperHyperEdge and with other terms, the Extreme R-List-Coloring with the inclusion of all Extreme SuperHyperVertices in one Extreme SuperHyperEdge, is an Extreme quasi-R-List-Coloring. To sum them up, in a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-List-Coloring minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-List-Coloring, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Extreme R-List-Coloring has two titles. an Extreme quasi-R-List-Coloring and its corresponded quasi-maximum Extreme R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Extreme number, there&#39;s an Extreme quasi-R-List-Coloring with that quasi-maximum Extreme SuperHyperCardinality in the terms of the embedded Extreme SuperHyperGraph. If there&#39;s an embedded Extreme SuperHyperGraph, then the Extreme quasi-SuperHyperNotions lead us to take the collection of all the Extreme quasi-R-List-Colorings for all Extreme numbers less than its Extreme corresponded maximum number. The essence of the Extreme List-Coloring ends up but this essence starts up in the terms of the Extreme quasi-R-List-Coloring, again and more in the operations of collecting all the Extreme quasi-R-List-Colorings acted on the all possible used formations of the Extreme SuperHyperGraph to achieve one Extreme number. This Extreme number is\\ considered as the equivalence class for all corresponded quasi-R-List-Colorings. Let $z_{\text{Extreme Number}},S_{\text{Extreme SuperHyperSet}}$ and $G_{\text{Extreme List-Coloring}}$ be an Extreme number, an Extreme SuperHyperSet and an Extreme List-Coloring. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Extreme Number}}]_{\text{Extreme Class}}=\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme List-Coloring}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Extreme List-Coloring is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme List-Coloring}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Extreme List-Coloring. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme List-Coloring}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Extreme List-Coloring poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme List-Coloring}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme List-Coloring}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Extreme SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Extreme SuperHyperVertices such that any amount of its Extreme SuperHyperVertices are incident to an Extreme&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Extreme&nbsp; Quasi-List-Coloring&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Extreme&nbsp; Quasi-List-Coloring&#39;&#39; since ``Extreme Quasi-List-Coloring&#39;&#39; happens ``Extreme List-Coloring&#39;&#39; in an Extreme SuperHyperGraph as initial framework and background but ``Extreme SuperHyperNeighborhood&#39;&#39; may not happens ``Extreme List-Coloring&#39;&#39; in an Extreme SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Extreme SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Extreme SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Extreme Quasi-List-Coloring&#39;&#39;, and&nbsp; ``Extreme List-Coloring&#39;&#39; are up. \\ Thus, let $z_{\text{Extreme Number}},N_{\text{Extreme SuperHyperNeighborhood}}$ and $G_{\text{Extreme List-Coloring}}$ be an Extreme number, an Extreme SuperHyperNeighborhood and an Extreme List-Coloring and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme List-Coloring}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-List-Coloring if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperVertices is the simple Extreme type-SuperHyperSet of the Extreme R-List-Coloring. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Extreme SuperHyperSet of Extreme SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Extreme type-SuperHyperSet of the Extreme R-List-Coloring. The Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Extreme R-List-Coloring}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is an Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of an Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no an Extreme&nbsp; SuperHyperEdge amid some Extreme SuperHyperVertices instead of all given by \underline{\textbf{Extreme List-Coloring}} is related to the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Extreme SuperHyperVertex \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme List-Coloring is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme List-Coloring is an Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Extreme SuperHyperVertex. But the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-List-Coloring \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-List-Coloring. Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Extreme R-List-Coloring $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no an Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme List-Coloring \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ List-Coloring}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; an Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no an Extreme SuperHyperEdge for some amount Extreme&nbsp; SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet called the&nbsp; Extreme List-Coloring. There isn&#39;t&nbsp; only less than two Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Extreme R-List-Coloring, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme List-Coloring, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Extreme SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; R-List-Coloring&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme R-List-Coloring}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Extreme SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only an Extreme free-triangle embedded SuperHyperModel and an Extreme on-triangle embedded SuperHyperModel but also it&#39;s an Extreme stable embedded SuperHyperModel. But all only non-obvious simple Extreme type-SuperHyperSets of the Extreme&nbsp; R-List-Coloring amid those obvious simple Extreme type-SuperHyperSets of the Extreme List-Coloring, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is an Extreme R-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of an Extreme&nbsp; R-List-Coloring is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-List-Coloring if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let an Extreme SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Extreme SuperHyperVertices $r.$ Consider all Extreme numbers of those Extreme SuperHyperVertices from that Extreme SuperHyperEdge excluding excluding more than $r$ distinct Extreme SuperHyperVertices, exclude to any given Extreme SuperHyperSet of the Extreme SuperHyperVertices. Consider there&#39;s an Extreme&nbsp; R-List-Coloring with the least cardinality, the lower sharp Extreme bound for Extreme cardinality. Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The Extreme SuperHyperSet of the Extreme SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is an Extreme SuperHyperSet $S$ of&nbsp; the Extreme SuperHyperVertices such that there&#39;s an Extreme SuperHyperEdge to have&nbsp; some Extreme SuperHyperVertices uniquely but it isn&#39;t an Extreme R-List-Coloring. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of an Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices such that there&#39;s an Extreme SuperHyperEdge to have some SuperHyperVertices uniquely. The Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices but it isn&#39;t an Extreme R-List-Coloring. Since it \textbf{\underline{doesn&#39;t do}} the Extreme procedure such that such that there&#39;s an Extreme SuperHyperEdge to have some Extreme&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Extreme SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Extreme SuperHyperGraph $ESHG:(V,E),$ an Extreme SuperHyperVertex, titled its Extreme SuperHyperNeighbor,&nbsp; to that Extreme SuperHyperVertex in the Extreme SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Extreme procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Extreme SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Extreme SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Extreme SuperHyperNeighborhood. Thus the obvious Extreme R-List-Coloring,&nbsp; $V_{ESHE}$ is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-List-Coloring,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} an Extreme SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Extreme SuperHyperVertices does forms any kind of Extreme pairs are titled&nbsp;&nbsp; \underline{Extreme SuperHyperNeighbors} in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Extreme SuperHyperCardinality}} of an Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s an Extreme SuperHyperEdge to have some Extreme SuperHyperVertices uniquely. Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Any Extreme R-List-Coloring only contains all interior Extreme SuperHyperVertices and all exterior Extreme SuperHyperVertices from the unique Extreme SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Extreme SuperHyperNeighbors in and there&#39;s all&nbsp; Extreme SuperHyperNeighborhoods in with no exception minus all&nbsp; Extreme SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Extreme SuperHyperNeighborhoods and Extreme SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; List-Coloring, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Extreme type-SuperHyperSet of the Extreme List-Coloring. &nbsp;The Extreme SuperHyperSet of Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Extreme type-SuperHyperSet of the Extreme List-Coloring. The Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Extreme List-Coloring}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is an Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of an Extreme SuperHyperSet $S$ of Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of an Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Extreme SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme List-Coloring is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme List-Coloring is an Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Extreme SuperHyperVertices. But the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme List-Coloring \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme List-Coloring. Since the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Extreme List-Coloring $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no an Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme List-Coloring \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ List-Coloring}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; an Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of an Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There aren&#39;t&nbsp; only less than three Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Extreme List-Coloring, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme List-Coloring, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Extreme SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; List-Coloring&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme List-Coloring}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{an Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperList-Coloring in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{an Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{an Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. Then there&#39;s no at least one SuperHyperList-Coloring. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperList-Coloring could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperList-Coloring taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperList-Coloring in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperList-Coloring taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperList-Coloring. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperList-Coloring could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{an Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperList-Coloring in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperList-Coloring taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. Then there&#39;s at least one SuperHyperList-Coloring. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperList-Coloring could be applied. The unique embedded SuperHyperList-Coloring proposes some longest SuperHyperList-Coloring excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{an Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperList-Coloring in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperList-Coloring,&nbsp; Extreme SuperHyperList-Coloring, and the Extreme SuperHyperList-Coloring, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperList-Coloring is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperList-Coloring. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperList-Coloring=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperList-Coloring of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperList-Coloring \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperList-Coloring.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperList-Coloring and SuperHyperList-Coloring coincide. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is an Extreme SuperHyperList-Coloring if and only if it&#39;s a SuperHyperList-Coloring. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperList-Coloring if and only if it&#39;s a longest SuperHyperList-Coloring. \end{corollary} \begin{corollary} Assume SuperHyperClasses of an Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperList-Coloring is its SuperHyperList-Coloring and reversely. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperList-Coloring is its SuperHyperList-Coloring and reversely. \end{corollary} \begin{corollary} &nbsp;Assume an Extreme SuperHyperGraph. Then its Extreme SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of an Extreme SuperHyperGraph. Then its Extreme SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume an Extreme SuperHyperGraph. Then its Extreme SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of an Extreme SuperHyperGraph. Then its Extreme SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} \begin{corollary} Assume an Extreme SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be an Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperList-Coloring/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperList-Coloring/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperList-Coloring; &nbsp; \item[$(ii):$] the SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperList-Coloring; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be an Extreme SuperHyperGraph which is SuperHyperList-Coloring/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be an Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperList-Coloring, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperList-Coloring, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperList-Coloring set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperList-Coloring. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperList-Coloring. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is an s-SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperList-Coloring, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperList-Coloring. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperList-Coloring. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperList-Coloring or the Extreme&nbsp;&nbsp; SuperHyperList-Coloring in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{an Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperList-Coloring} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperList-Coloring. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{an Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperList-Coloring} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperList-Coloring. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperList-Coloring and the Extreme&nbsp;&nbsp; SuperHyperList-Coloring are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperList-Coloring and the Extreme&nbsp;&nbsp; SuperHyperList-Coloring? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperList-Coloring and the Extreme&nbsp;&nbsp; SuperHyperList-Coloring? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperList-Coloring and the Extreme&nbsp;&nbsp; SuperHyperList-Coloring do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperList-Coloring, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperList-Coloring. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperList-Coloring, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperList-Coloring, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperList-Coloring and the Extreme&nbsp;&nbsp; SuperHyperList-Coloring. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperList-Coloring&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperList-Coloring}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperList-Coloring}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider an Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume an Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#188 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Cliff By Hyper Cling Of Clique-Cut In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.27392.30721). @ResearchGate: https://www.researchgate.net/publication/369151536 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Cliff By Hyper Cling Of Clique-Cut In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Cut). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Cut pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Cut if the following expression is called Neutrosophic e-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*}&nbsp; Neutrosophic re-SuperHyperClique-Cut if the following expression is called Neutrosophic e-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Cut&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Cut if the following expression is called Neutrosophic v-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut. ((Neutrosophic) SuperHyperClique-Cut). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; a Neutrosophic SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; an Extreme SuperHyperClique-Cut SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; a Neutrosophic V-SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; an Extreme V-SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Cut &nbsp;and Neutrosophic SuperHyperClique-Cut. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Cut is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Cut is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Cut . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Cut &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Cut . It&#39;s redefined a Neutrosophic SuperHyperClique-Cut &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Cut . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Cut until the SuperHyperClique-Cut, then it&#39;s officially called a ``SuperHyperClique-Cut&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Cut . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Cut &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Cut . For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; and a ``Neutrosophic SuperHyperClique-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Cut &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Cut &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Cut&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Cut &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Cut .] SuperHyperClique-Cut . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Cut if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Cut &nbsp;or the strongest SuperHyperClique-Cut &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Cut, called SuperHyperClique-Cut, and the strongest SuperHyperClique-Cut, called Neutrosophic SuperHyperClique-Cut, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Cut. There isn&#39;t any formation of any SuperHyperClique-Cut but literarily, it&#39;s the deformation of any SuperHyperClique-Cut. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Cut theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} SuperHyperGraph, SuperHyperClique-Cut, Cancer&#39;s Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Cut or the Extreme&nbsp;&nbsp; SuperHyperClique-Cut in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Cut. There isn&#39;t any formation of any SuperHyperClique-Cut but literarily, it&#39;s the deformation of any SuperHyperClique-Cut. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Cut&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Cut and Extreme&nbsp;&nbsp; SuperHyperClique-Cut, are figured out in sections ``&nbsp; SuperHyperClique-Cut&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39;. In the sense of tackling on getting results and in Clique-Cut to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Cut&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Cut&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Cut of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Cut of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Cut} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Cut such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Cut such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Cut. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Cut more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Cut&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Cut. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Cut} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperClique-Cut But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Any k-function Clique-Cut like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function Clique-Cut like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $m$ and $n$ propose special Clique-Cut. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability Clique-Cut $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Extreme Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Cut $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X_n$ be a Extreme Variable in a probability Clique-Cut (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_1,V_2,V_3,N,F\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=(\text{Four Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i,V_{13}\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{13},V_i\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_i,V_{13}\}_{i=1}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}}= 2z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; =5z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}}=11z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{V_i\in E_2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z^{7}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(\text{Ten Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1,V_i\}_{V_i\in E_6}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =|E_6|z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{M_6,L_6,F,V_3,V_2,H_6,O_6,E_6,C_6,Z_5,W_5,V_{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{12}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Cut minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Cut, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Cut is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Cut in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Cut. \end{proposition} \begin{proposition} &nbsp;Assume a simple Extreme SuperHyperGraph $ESHG:(V,E).$ Then the Extreme number of&nbsp; type-result-R-Clique-Cut has, the least Extreme cardinality, the lower sharp Extreme bound for Extreme cardinality, is the Extreme cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Extreme type-result-R-Clique-Cut with the least Extreme cardinality, the lower sharp Extreme bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Extreme type-result-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme type-result-Clique-Cut is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Cut since neither amount of Extreme SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Extreme number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Extreme SuperHyperSet of the Extreme SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices but the maximum Extreme cardinality indicates that these Extreme&nbsp; type-SuperHyperSets couldn&#39;t give us the Extreme lower bound in the term of Extreme sharpness. In other words, the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Extreme SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Extreme SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Extreme SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Cut is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Extreme SuperHyperClasses of the connected loopless Extreme SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Cut. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Extreme SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Extreme structure of the Extreme R-Clique-Cut decorates the Extreme SuperHyperVertices don&#39;t have received any Extreme connections so as this Extreme style implies different versions of Extreme SuperHyperEdges with the maximum Extreme cardinality in the terms of Extreme SuperHyperVertices are spotlight. The lower Extreme bound is to have the maximum Extreme groups of Extreme SuperHyperVertices have perfect Extreme connections inside each of SuperHyperEdges and the outside of this Extreme SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Extreme SuperHyperGraph arising from its Extreme properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Extreme SuperHyperVertex in the targeted Extreme SuperHyperSet, then there&#39;s no Extreme connection. Furthermore, the Extreme existence of one Extreme SuperHyperVertex has no&nbsp; Extreme effect to talk about the Extreme R-Clique-Cut. Since at least two Extreme SuperHyperVertices involve to make a title in the Extreme background of the Extreme SuperHyperGraph. The Extreme SuperHyperGraph is obvious if it has no Extreme SuperHyperEdge but at least two Extreme SuperHyperVertices make the Extreme version of Extreme SuperHyperEdge. Thus in the Extreme setting of non-obvious Extreme SuperHyperGraph, there are at least one Extreme SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Extreme adjective for the initial Extreme SuperHyperGraph, induces there&#39;s no Extreme&nbsp; appearance of the loop Extreme version of the Extreme SuperHyperEdge and this Extreme SuperHyperGraph is said to be loopless. The Extreme adjective ``loop&#39;&#39; on the basic Extreme framework engages one Extreme SuperHyperVertex but it never happens in this Extreme setting. With these Extreme bases, on a Extreme SuperHyperGraph, there&#39;s at least one Extreme SuperHyperEdge thus there&#39;s at least a Extreme R-Clique-Cut has the Extreme cardinality of a Extreme SuperHyperEdge. Thus, a Extreme R-Clique-Cut has the Extreme cardinality at least a Extreme SuperHyperEdge. Assume a Extreme SuperHyperSet $V\setminus V\setminus \{z\}.$ This Extreme SuperHyperSet isn&#39;t a Extreme R-Clique-Cut since either the Extreme SuperHyperGraph is an obvious Extreme SuperHyperModel thus it never happens since there&#39;s no Extreme usage of this Extreme framework and even more there&#39;s no Extreme connection inside or the Extreme SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Extreme contradiction with the term ``Extreme R-Clique-Cut&#39;&#39; since the maximum Extreme cardinality never happens for this Extreme style of the Extreme SuperHyperSet and beyond that there&#39;s no Extreme connection inside as mentioned in first Extreme case in the forms of drawback for this selected Extreme SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Extreme case implies having the Extreme style of on-quasi-triangle Extreme style on the every Extreme elements of this Extreme SuperHyperSet. Precisely, the Extreme R-Clique-Cut is the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that some Extreme amount of the Extreme SuperHyperVertices are on-quasi-triangle Extreme style. The Extreme cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Extreme bound is up. Thus the minimum Extreme cardinality of the maximum Extreme cardinality ends up the Extreme discussion. The first Extreme term refers to the Extreme setting of the Extreme SuperHyperGraph but this key point is enough since there&#39;s a Extreme SuperHyperClass of a Extreme SuperHyperGraph has no on-quasi-triangle Extreme style amid some amount of its Extreme SuperHyperVertices. This Extreme setting of the Extreme SuperHyperModel proposes a Extreme SuperHyperSet has only some amount&nbsp; Extreme SuperHyperVertices from one Extreme SuperHyperEdge such that there&#39;s no Extreme amount of Extreme SuperHyperEdges more than one involving these some amount of these Extreme SuperHyperVertices. The Extreme cardinality of this Extreme SuperHyperSet is the maximum and the Extreme case is occurred in the minimum Extreme situation. To sum them up, the Extreme SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Extreme cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Extreme SuperHyperVertices such that there&#39;s distinct-covers-order-amount Extreme SuperHyperEdges for amount of Extreme SuperHyperVertices taken from the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Extreme SuperHyperSet of the Extreme SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Extreme&nbsp; R-Clique-Cut for the Extreme SuperHyperGraph as used Extreme background in the Extreme terms of worst Extreme case and the common theme of the lower Extreme bound occurred in the specific Extreme SuperHyperClasses of the Extreme SuperHyperGraphs which are Extreme free-quasi-triangle. &nbsp; \\ Assume a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Extreme number of the Extreme SuperHyperVertices. Then every Extreme SuperHyperVertex has at least no Extreme SuperHyperEdge with others in common. Thus those Extreme SuperHyperVertices have the eligibles to be contained in a Extreme R-Clique-Cut. Those Extreme SuperHyperVertices are potentially included in a Extreme&nbsp; style-R-Clique-Cut. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Extreme SuperHyperVertices of a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Extreme&nbsp; SuperHyperVertices of the Extreme SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices and there&#39;s only and only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Extreme SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Extreme R-Clique-Cut is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Extreme R-Clique-Cut but with slightly differences in the maximum Extreme cardinality amid those Extreme type-SuperHyperSets of the Extreme SuperHyperVertices. Thus the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Extreme cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Extreme R-Clique-Cut. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices belong to the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Cut}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Cut}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Extreme quasi-R-Clique-Cut where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Extreme intended SuperHyperVertices but in a Extreme Clique-Cut, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Cut is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Cut in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Cut. \\ The obvious SuperHyperGraph has no Extreme SuperHyperEdges. But the non-obvious Extreme SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Extreme optimal SuperHyperObject. It specially delivers some remarks on the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that there&#39;s distinct amount of Extreme SuperHyperEdges for distinct amount of Extreme SuperHyperVertices up to all&nbsp; taken from that Extreme SuperHyperSet of the Extreme SuperHyperVertices but this Extreme SuperHyperSet of the Extreme SuperHyperVertices is either has the maximum Extreme SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Extreme SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Extreme SuperHyperEdge containing at least all Extreme SuperHyperVertices. Thus it forms a Extreme quasi-R-Clique-Cut where the Extreme completion of the Extreme incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Extreme embedded R-Clique-Cut. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Extreme SuperHyperCardinality and they&#39;re Extreme SuperHyperOptimal. The less than two distinct types of Extreme SuperHyperVertices are included in the minimum Extreme style of the embedded Extreme R-Clique-Cut. The interior types of the Extreme SuperHyperVertices are deciders. Since the Extreme number of SuperHyperNeighbors are only&nbsp; affected by the interior Extreme SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Extreme SuperHyperSet for any distinct types of Extreme SuperHyperVertices pose the Extreme R-Clique-Cut. Thus Extreme exterior SuperHyperVertices could be used only in one Extreme SuperHyperEdge and in Extreme SuperHyperRelation with the interior Extreme SuperHyperVertices in that&nbsp; Extreme SuperHyperEdge. In the embedded Extreme Clique-Cut, there&#39;s the usage of exterior Extreme SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Extreme SuperHyperVertex has no connection, inside. Thus, the Extreme SuperHyperSet of the Extreme SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Extreme R-Clique-Cut. The Extreme R-Clique-Cut with the exclusion of the exclusion of all&nbsp; Extreme SuperHyperVertices in one Extreme SuperHyperEdge and with other terms, the Extreme R-Clique-Cut with the inclusion of all Extreme SuperHyperVertices in one Extreme SuperHyperEdge, is a Extreme quasi-R-Clique-Cut. To sum them up, in a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Cut minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Cut, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Extreme R-Clique-Cut has two titles. a Extreme quasi-R-Clique-Cut and its corresponded quasi-maximum Extreme R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Extreme number, there&#39;s a Extreme quasi-R-Clique-Cut with that quasi-maximum Extreme SuperHyperCardinality in the terms of the embedded Extreme SuperHyperGraph. If there&#39;s an embedded Extreme SuperHyperGraph, then the Extreme quasi-SuperHyperNotions lead us to take the collection of all the Extreme quasi-R-Clique-Cuts for all Extreme numbers less than its Extreme corresponded maximum number. The essence of the Extreme Clique-Cut ends up but this essence starts up in the terms of the Extreme quasi-R-Clique-Cut, again and more in the operations of collecting all the Extreme quasi-R-Clique-Cuts acted on the all possible used formations of the Extreme SuperHyperGraph to achieve one Extreme number. This Extreme number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Cuts. Let $z_{\text{Extreme Number}},S_{\text{Extreme SuperHyperSet}}$ and $G_{\text{Extreme Clique-Cut}}$ be a Extreme number, a Extreme SuperHyperSet and a Extreme Clique-Cut. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Extreme Number}}]_{\text{Extreme Class}}=\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Extreme Clique-Cut is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Extreme Clique-Cut. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Extreme Clique-Cut poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Extreme SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Extreme SuperHyperVertices such that any amount of its Extreme SuperHyperVertices are incident to a Extreme&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Extreme&nbsp; Quasi-Clique-Cut&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Extreme&nbsp; Quasi-Clique-Cut&#39;&#39; since ``Extreme Quasi-Clique-Cut&#39;&#39; happens ``Extreme Clique-Cut&#39;&#39; in a Extreme SuperHyperGraph as initial framework and background but ``Extreme SuperHyperNeighborhood&#39;&#39; may not happens ``Extreme Clique-Cut&#39;&#39; in a Extreme SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Extreme SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Extreme SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Extreme Quasi-Clique-Cut&#39;&#39;, and&nbsp; ``Extreme Clique-Cut&#39;&#39; are up. \\ Thus, let $z_{\text{Extreme Number}},N_{\text{Extreme SuperHyperNeighborhood}}$ and $G_{\text{Extreme Clique-Cut}}$ be a Extreme number, a Extreme SuperHyperNeighborhood and a Extreme Clique-Cut and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperVertices is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Cut. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Extreme SuperHyperSet of Extreme SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Cut. The Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Extreme R-Clique-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge amid some Extreme SuperHyperVertices instead of all given by \underline{\textbf{Extreme Clique-Cut}} is related to the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Extreme SuperHyperVertex \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Cut is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Cut is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Extreme SuperHyperVertex. But the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Cut \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Cut. Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Extreme R-Clique-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme SuperHyperEdge for some amount Extreme&nbsp; SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Cut. There isn&#39;t&nbsp; only less than two Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Extreme R-Clique-Cut, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Cut, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Extreme SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; R-Clique-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme R-Clique-Cut}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Extreme SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Extreme free-triangle embedded SuperHyperModel and a Extreme on-triangle embedded SuperHyperModel but also it&#39;s a Extreme stable embedded SuperHyperModel. But all only non-obvious simple Extreme type-SuperHyperSets of the Extreme&nbsp; R-Clique-Cut amid those obvious simple Extreme type-SuperHyperSets of the Extreme Clique-Cut, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Extreme R-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme&nbsp; R-Clique-Cut is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Extreme SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Extreme SuperHyperVertices $r.$ Consider all Extreme numbers of those Extreme SuperHyperVertices from that Extreme SuperHyperEdge excluding excluding more than $r$ distinct Extreme SuperHyperVertices, exclude to any given Extreme SuperHyperSet of the Extreme SuperHyperVertices. Consider there&#39;s a Extreme&nbsp; R-Clique-Cut with the least cardinality, the lower sharp Extreme bound for Extreme cardinality. Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The Extreme SuperHyperSet of the Extreme SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Extreme SuperHyperSet $S$ of&nbsp; the Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have&nbsp; some Extreme SuperHyperVertices uniquely but it isn&#39;t a Extreme R-Clique-Cut. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have some SuperHyperVertices uniquely. The Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Extreme cardinality of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices but it isn&#39;t a Extreme R-Clique-Cut. Since it \textbf{\underline{doesn&#39;t do}} the Extreme procedure such that such that there&#39;s a Extreme SuperHyperEdge to have some Extreme&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Extreme SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Extreme SuperHyperGraph $ESHG:(V,E),$ a Extreme SuperHyperVertex, titled its Extreme SuperHyperNeighbor,&nbsp; to that Extreme SuperHyperVertex in the Extreme SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Extreme procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Extreme SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Extreme SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Extreme SuperHyperNeighborhood. Thus the obvious Extreme R-Clique-Cut,&nbsp; $V_{ESHE}$ is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Cut,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Extreme SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Extreme SuperHyperVertices does forms any kind of Extreme pairs are titled&nbsp;&nbsp; \underline{Extreme SuperHyperNeighbors} in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Extreme SuperHyperCardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Extreme SuperHyperEdge to have some Extreme SuperHyperVertices uniquely. Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Any Extreme R-Clique-Cut only contains all interior Extreme SuperHyperVertices and all exterior Extreme SuperHyperVertices from the unique Extreme SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Extreme SuperHyperNeighbors in and there&#39;s all&nbsp; Extreme SuperHyperNeighborhoods in with no exception minus all&nbsp; Extreme SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Extreme SuperHyperNeighborhoods and Extreme SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Cut, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Extreme type-SuperHyperSet of the Extreme Clique-Cut. &nbsp;The Extreme SuperHyperSet of Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Extreme type-SuperHyperSet of the Extreme Clique-Cut. The Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Extreme Clique-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Extreme SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Cut is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Cut is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Extreme SuperHyperVertices. But the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Cut \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Cut. Since the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Extreme Clique-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There aren&#39;t&nbsp; only less than three Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Extreme Clique-Cut, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Cut, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Extreme SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; Clique-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme Clique-Cut}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperClique-Cut in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^2. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}| \text{Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Cut could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Cut taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Cut in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{|P_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^{|P_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Cut taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Cut could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperClique-Cut in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E^{*}_1,E^{*}_2,E^{*}_3\}_{E^{*}_i\in E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E^{*}_{NSHG}| \text{Choose Three})z^3. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Cut taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Cut. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Cut could be applied. The unique embedded SuperHyperClique-Cut proposes some longest SuperHyperClique-Cut excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Cut in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Cut,&nbsp; Extreme SuperHyperClique-Cut, and the Extreme SuperHyperClique-Cut, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperClique-Cut is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperClique-Cut. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperClique-Cut=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Cut of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Cut \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperClique-Cut.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperClique-Cut and SuperHyperClique-Cut coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperClique-Cut if and only if it&#39;s a SuperHyperClique-Cut. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Cut if and only if it&#39;s a longest SuperHyperClique-Cut. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Cut is its SuperHyperClique-Cut and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Cut is its SuperHyperClique-Cut and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Cut/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Cut/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Cut; &nbsp; \item[$(ii):$] the SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Cut; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperClique-Cut/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Cut, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Cut, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Cut set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Cut, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperClique-Cut or the Extreme&nbsp;&nbsp; SuperHyperClique-Cut in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Cut} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperClique-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Cut} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperClique-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Cut and the Extreme&nbsp;&nbsp; SuperHyperClique-Cut are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Cut and the Extreme&nbsp;&nbsp; SuperHyperClique-Cut? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Cut and the Extreme&nbsp;&nbsp; SuperHyperClique-Cut? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Cut and the Extreme&nbsp;&nbsp; SuperHyperClique-Cut do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Cut, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Cut. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperClique-Cut, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Cut, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Cut and the Extreme&nbsp;&nbsp; SuperHyperClique-Cut. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Cut}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperClique-Cut}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

Henry Garrett, &ldquo;New Ideas On Super Decompensation By Hyper Decompress Of Clique-Decompositions In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.27169.48487). @ResearchGate: https://www.researchgate.net/publication/369186444 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Decompensation&nbsp; By Hyper Decompress Of Clique-Decompositions In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Decompositions). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Decompositions pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Decompositions if the following expression is called Neutrosophic e-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp;Neutrosophic re-SuperHyperClique-Decompositions if the following expression is called Neutrosophic e-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Decompositions&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Decompositions if the following expression is called Neutrosophic v-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions. ((Neutrosophic) SuperHyperClique-Decompositions). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; a Neutrosophic SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; an Extreme SuperHyperClique-Decompositions SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; a Neutrosophic V-SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; an Extreme V-SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Decompositions &nbsp;and Neutrosophic SuperHyperClique-Decompositions. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Decompositions is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Decompositions is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Decompositions . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Decompositions &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Decompositions &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Decompositions . It&#39;s redefined a Neutrosophic SuperHyperClique-Decompositions &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Decompositions . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Decompositions until the SuperHyperClique-Decompositions, then it&#39;s officially called a ``SuperHyperClique-Decompositions&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Decompositions . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Decompositions &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Decompositions . For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; and a ``Neutrosophic SuperHyperClique-Decompositions &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Decompositions &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Decompositions &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Decompositions &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Decompositions .] SuperHyperClique-Decompositions . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Decompositions if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Decompositions &nbsp;or the strongest SuperHyperClique-Decompositions &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Decompositions, called SuperHyperClique-Decompositions, and the strongest SuperHyperClique-Decompositions, called Neutrosophic SuperHyperClique-Decompositions, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Decompositions. There isn&#39;t any formation of any SuperHyperClique-Decompositions but literarily, it&#39;s the deformation of any SuperHyperClique-Decompositions. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Decompositions theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperClique-Decompositions, Cancer&#39;s&nbsp; Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Decompositions or the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Decompositions. There isn&#39;t any formation of any SuperHyperClique-Decompositions but literarily, it&#39;s the deformation of any SuperHyperClique-Decompositions. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Decompositions and Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions, are figured out in sections ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39;. In the sense of tackling on getting results and in Clique-Decompositions to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Decompositions&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Decompositions&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Decompositions of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Decompositions of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Decompositions} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Decompositions} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Decompositions such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Decompositions} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Decompositions such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Decompositions. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Decompositions more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Decompositions. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Decompositions} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperClique-Decompositions But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Any k-function Clique-Decompositions like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function Clique-Decompositions like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $m$ and $n$ propose special Clique-Decompositions. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability Clique-Decompositions $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Extreme Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Decompositions $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X_n$ be a Extreme Variable in a probability Clique-Decompositions (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Decompositions. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperClique-Decompositions. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{\{E_4\},\{E_5\},\{E_1,E_4\},\{E_1,E_5\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}}=2z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1,V_2,V_3,N,F,V_4\}.\{V_1,V_2,V_3,N,F,H\},\{V_1,V_2,V_3,N,F,O\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =3z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\}_{i\neq j\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=(\text{Four Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{i=1}^5,\{V_i\}_{i=5}^8,\dots\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5+2z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{E_1,E_2\},\ldots\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7,\ldots\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8+z^7. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{V_i,V_{13}\}_{i=4}^7,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^4. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{V_{13},V_i\}_{i=4}^7,\{V_{14},V_i\}_{i=8}^{11},\{V_{12},V_i\}_{i=1}^3,\{V_i\}_{i=12}^{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{E_i,E_{i+1}\}_{i=1}^{10}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{V_i,V_{i+1}\}_{i=1}^{10},\{V_i,V_{22}\}_{i=11}^{20}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =az^2+z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6,\{E_4,E_5,E_6\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^1+z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_{13},V_i\}_{i=4}^7,\{V_{14},V_i\}_{i=8}^{11},\{V_{12},V_i\}_{i=1}^3,\{V_i\}_{i=12}^{14}\}. &nbsp;\\&amp;&amp; &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_2,E_3,E_4,E_5\},\{E_2,E_4,E_5\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^4+z^3+az^2+7z. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{\{V_4,V_5,V_6\},\{V_1,V_2,V_3\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3+az^2+6z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}=\{E_1,\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=az^2+6z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^5+az^2+10z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_2,E_3,E_4,E_5\},\{E_2,E_4,E_5\},\{E_1,E_9,E_{10}\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^4+2z^3+az^2+10z. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{\{V_4,V_5,V_6\},\{V_1,V_2,V_3\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3+az^2+6z. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}}=\{\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}}= 2z^2+3z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; =5z^2+6z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+12z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_8},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{9}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_6},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =az^{b}+\ldots+kz. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2+2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_2},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+10z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperClique-Decompositions, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2,E_3\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^3+az^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_3},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{12}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Decompositions minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Decompositions, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Decompositions is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Decompositions is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Decompositions in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Decompositions. \end{proposition} \begin{proposition} &nbsp;Assume a simple Extreme SuperHyperGraph $ESHG:(V,E).$ Then the Extreme number of&nbsp; type-result-R-Clique-Decompositions has, the least Extreme cardinality, the lower sharp Extreme bound for Extreme cardinality, is the Extreme cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Extreme type-result-R-Clique-Decompositions with the least Extreme cardinality, the lower sharp Extreme bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Extreme type-result-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme type-result-Clique-Decompositions is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Decompositions since neither amount of Extreme SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Extreme number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Extreme SuperHyperSet of the Extreme SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices but the maximum Extreme cardinality indicates that these Extreme&nbsp; type-SuperHyperSets couldn&#39;t give us the Extreme lower bound in the term of Extreme sharpness. In other words, the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Extreme SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Extreme SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Extreme SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Decompositions is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Extreme SuperHyperClasses of the connected loopless Extreme SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Decompositions. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Extreme SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Extreme structure of the Extreme R-Clique-Decompositions decorates the Extreme SuperHyperVertices don&#39;t have received any Extreme connections so as this Extreme style implies different versions of Extreme SuperHyperEdges with the maximum Extreme cardinality in the terms of Extreme SuperHyperVertices are spotlight. The lower Extreme bound is to have the maximum Extreme groups of Extreme SuperHyperVertices have perfect Extreme connections inside each of SuperHyperEdges and the outside of this Extreme SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Extreme SuperHyperGraph arising from its Extreme properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Extreme SuperHyperVertex in the targeted Extreme SuperHyperSet, then there&#39;s no Extreme connection. Furthermore, the Extreme existence of one Extreme SuperHyperVertex has no&nbsp; Extreme effect to talk about the Extreme R-Clique-Decompositions. Since at least two Extreme SuperHyperVertices involve to make a title in the Extreme background of the Extreme SuperHyperGraph. The Extreme SuperHyperGraph is obvious if it has no Extreme SuperHyperEdge but at least two Extreme SuperHyperVertices make the Extreme version of Extreme SuperHyperEdge. Thus in the Extreme setting of non-obvious Extreme SuperHyperGraph, there are at least one Extreme SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Extreme adjective for the initial Extreme SuperHyperGraph, induces there&#39;s no Extreme&nbsp; appearance of the loop Extreme version of the Extreme SuperHyperEdge and this Extreme SuperHyperGraph is said to be loopless. The Extreme adjective ``loop&#39;&#39; on the basic Extreme framework engages one Extreme SuperHyperVertex but it never happens in this Extreme setting. With these Extreme bases, on a Extreme SuperHyperGraph, there&#39;s at least one Extreme SuperHyperEdge thus there&#39;s at least a Extreme R-Clique-Decompositions has the Extreme cardinality of a Extreme SuperHyperEdge. Thus, a Extreme R-Clique-Decompositions has the Extreme cardinality at least a Extreme SuperHyperEdge. Assume a Extreme SuperHyperSet $V\setminus V\setminus \{z\}.$ This Extreme SuperHyperSet isn&#39;t a Extreme R-Clique-Decompositions since either the Extreme SuperHyperGraph is an obvious Extreme SuperHyperModel thus it never happens since there&#39;s no Extreme usage of this Extreme framework and even more there&#39;s no Extreme connection inside or the Extreme SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Extreme contradiction with the term ``Extreme R-Clique-Decompositions&#39;&#39; since the maximum Extreme cardinality never happens for this Extreme style of the Extreme SuperHyperSet and beyond that there&#39;s no Extreme connection inside as mentioned in first Extreme case in the forms of drawback for this selected Extreme SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Extreme case implies having the Extreme style of on-quasi-triangle Extreme style on the every Extreme elements of this Extreme SuperHyperSet. Precisely, the Extreme R-Clique-Decompositions is the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that some Extreme amount of the Extreme SuperHyperVertices are on-quasi-triangle Extreme style. The Extreme cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Extreme bound is up. Thus the minimum Extreme cardinality of the maximum Extreme cardinality ends up the Extreme discussion. The first Extreme term refers to the Extreme setting of the Extreme SuperHyperGraph but this key point is enough since there&#39;s a Extreme SuperHyperClass of a Extreme SuperHyperGraph has no on-quasi-triangle Extreme style amid some amount of its Extreme SuperHyperVertices. This Extreme setting of the Extreme SuperHyperModel proposes a Extreme SuperHyperSet has only some amount&nbsp; Extreme SuperHyperVertices from one Extreme SuperHyperEdge such that there&#39;s no Extreme amount of Extreme SuperHyperEdges more than one involving these some amount of these Extreme SuperHyperVertices. The Extreme cardinality of this Extreme SuperHyperSet is the maximum and the Extreme case is occurred in the minimum Extreme situation. To sum them up, the Extreme SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Extreme cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Extreme SuperHyperVertices such that there&#39;s distinct-covers-order-amount Extreme SuperHyperEdges for amount of Extreme SuperHyperVertices taken from the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Extreme SuperHyperSet of the Extreme SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Extreme&nbsp; R-Clique-Decompositions for the Extreme SuperHyperGraph as used Extreme background in the Extreme terms of worst Extreme case and the common theme of the lower Extreme bound occurred in the specific Extreme SuperHyperClasses of the Extreme SuperHyperGraphs which are Extreme free-quasi-triangle. &nbsp; \\ Assume a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Extreme number of the Extreme SuperHyperVertices. Then every Extreme SuperHyperVertex has at least no Extreme SuperHyperEdge with others in common. Thus those Extreme SuperHyperVertices have the eligibles to be contained in a Extreme R-Clique-Decompositions. Those Extreme SuperHyperVertices are potentially included in a Extreme&nbsp; style-R-Clique-Decompositions. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Extreme SuperHyperVertices of a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Extreme&nbsp; SuperHyperVertices of the Extreme SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices and there&#39;s only and only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Extreme SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Extreme R-Clique-Decompositions is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Extreme R-Clique-Decompositions but with slightly differences in the maximum Extreme cardinality amid those Extreme type-SuperHyperSets of the Extreme SuperHyperVertices. Thus the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Extreme cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Extreme R-Clique-Decompositions. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices belong to the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Decompositions}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Clique-Decompositions}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Extreme quasi-R-Clique-Decompositions where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Extreme intended SuperHyperVertices but in a Extreme Clique-Decompositions, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Clique-Decompositions is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Clique-Decompositions is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Clique-Decompositions in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Clique-Decompositions. \\ The obvious SuperHyperGraph has no Extreme SuperHyperEdges. But the non-obvious Extreme SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Extreme optimal SuperHyperObject. It specially delivers some remarks on the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that there&#39;s distinct amount of Extreme SuperHyperEdges for distinct amount of Extreme SuperHyperVertices up to all&nbsp; taken from that Extreme SuperHyperSet of the Extreme SuperHyperVertices but this Extreme SuperHyperSet of the Extreme SuperHyperVertices is either has the maximum Extreme SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Extreme SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Extreme SuperHyperEdge containing at least all Extreme SuperHyperVertices. Thus it forms a Extreme quasi-R-Clique-Decompositions where the Extreme completion of the Extreme incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Extreme embedded R-Clique-Decompositions. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Extreme SuperHyperCardinality and they&#39;re Extreme SuperHyperOptimal. The less than two distinct types of Extreme SuperHyperVertices are included in the minimum Extreme style of the embedded Extreme R-Clique-Decompositions. The interior types of the Extreme SuperHyperVertices are deciders. Since the Extreme number of SuperHyperNeighbors are only&nbsp; affected by the interior Extreme SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Extreme SuperHyperSet for any distinct types of Extreme SuperHyperVertices pose the Extreme R-Clique-Decompositions. Thus Extreme exterior SuperHyperVertices could be used only in one Extreme SuperHyperEdge and in Extreme SuperHyperRelation with the interior Extreme SuperHyperVertices in that&nbsp; Extreme SuperHyperEdge. In the embedded Extreme Clique-Decompositions, there&#39;s the usage of exterior Extreme SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Extreme SuperHyperVertex has no connection, inside. Thus, the Extreme SuperHyperSet of the Extreme SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Extreme R-Clique-Decompositions. The Extreme R-Clique-Decompositions with the exclusion of the exclusion of all&nbsp; Extreme SuperHyperVertices in one Extreme SuperHyperEdge and with other terms, the Extreme R-Clique-Decompositions with the inclusion of all Extreme SuperHyperVertices in one Extreme SuperHyperEdge, is a Extreme quasi-R-Clique-Decompositions. To sum them up, in a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Clique-Decompositions minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Clique-Decompositions, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Extreme R-Clique-Decompositions has two titles. a Extreme quasi-R-Clique-Decompositions and its corresponded quasi-maximum Extreme R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Extreme number, there&#39;s a Extreme quasi-R-Clique-Decompositions with that quasi-maximum Extreme SuperHyperCardinality in the terms of the embedded Extreme SuperHyperGraph. If there&#39;s an embedded Extreme SuperHyperGraph, then the Extreme quasi-SuperHyperNotions lead us to take the collection of all the Extreme quasi-R-Clique-Decompositionss for all Extreme numbers less than its Extreme corresponded maximum number. The essence of the Extreme Clique-Decompositions ends up but this essence starts up in the terms of the Extreme quasi-R-Clique-Decompositions, again and more in the operations of collecting all the Extreme quasi-R-Clique-Decompositionss acted on the all possible used formations of the Extreme SuperHyperGraph to achieve one Extreme number. This Extreme number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Decompositionss. Let $z_{\text{Extreme Number}},S_{\text{Extreme SuperHyperSet}}$ and $G_{\text{Extreme Clique-Decompositions}}$ be a Extreme number, a Extreme SuperHyperSet and a Extreme Clique-Decompositions. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Extreme Number}}]_{\text{Extreme Class}}=\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Extreme Clique-Decompositions is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Extreme Clique-Decompositions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Extreme Clique-Decompositions poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Extreme SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Extreme SuperHyperVertices such that any amount of its Extreme SuperHyperVertices are incident to a Extreme&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Extreme&nbsp; Quasi-Clique-Decompositions&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Extreme&nbsp; Quasi-Clique-Decompositions&#39;&#39; since ``Extreme Quasi-Clique-Decompositions&#39;&#39; happens ``Extreme Clique-Decompositions&#39;&#39; in a Extreme SuperHyperGraph as initial framework and background but ``Extreme SuperHyperNeighborhood&#39;&#39; may not happens ``Extreme Clique-Decompositions&#39;&#39; in a Extreme SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Extreme SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Extreme SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Extreme Quasi-Clique-Decompositions&#39;&#39;, and&nbsp; ``Extreme Clique-Decompositions&#39;&#39; are up. \\ Thus, let $z_{\text{Extreme Number}},N_{\text{Extreme SuperHyperNeighborhood}}$ and $G_{\text{Extreme Clique-Decompositions}}$ be a Extreme number, a Extreme SuperHyperNeighborhood and a Extreme Clique-Decompositions and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperVertices is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Decompositions. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Extreme SuperHyperSet of Extreme SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Extreme type-SuperHyperSet of the Extreme R-Clique-Decompositions. The Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Extreme R-Clique-Decompositions}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge amid some Extreme SuperHyperVertices instead of all given by \underline{\textbf{Extreme Clique-Decompositions}} is related to the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Extreme SuperHyperVertex \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Decompositions is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Decompositions is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Extreme SuperHyperVertex. But the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Decompositions \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Decompositions. Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Extreme R-Clique-Decompositions $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Decompositions \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Decompositions}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme SuperHyperEdge for some amount Extreme&nbsp; SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Decompositions. There isn&#39;t&nbsp; only less than two Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Extreme R-Clique-Decompositions, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Decompositions, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Extreme SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; R-Clique-Decompositions&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme R-Clique-Decompositions}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Extreme SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Extreme free-triangle embedded SuperHyperModel and a Extreme on-triangle embedded SuperHyperModel but also it&#39;s a Extreme stable embedded SuperHyperModel. But all only non-obvious simple Extreme type-SuperHyperSets of the Extreme&nbsp; R-Clique-Decompositions amid those obvious simple Extreme type-SuperHyperSets of the Extreme Clique-Decompositions, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Extreme R-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme&nbsp; R-Clique-Decompositions is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Extreme SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Extreme SuperHyperVertices $r.$ Consider all Extreme numbers of those Extreme SuperHyperVertices from that Extreme SuperHyperEdge excluding excluding more than $r$ distinct Extreme SuperHyperVertices, exclude to any given Extreme SuperHyperSet of the Extreme SuperHyperVertices. Consider there&#39;s a Extreme&nbsp; R-Clique-Decompositions with the least cardinality, the lower sharp Extreme bound for Extreme cardinality. Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The Extreme SuperHyperSet of the Extreme SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Extreme SuperHyperSet $S$ of&nbsp; the Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have&nbsp; some Extreme SuperHyperVertices uniquely but it isn&#39;t a Extreme R-Clique-Decompositions. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have some SuperHyperVertices uniquely. The Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Extreme cardinality of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices but it isn&#39;t a Extreme R-Clique-Decompositions. Since it \textbf{\underline{doesn&#39;t do}} the Extreme procedure such that such that there&#39;s a Extreme SuperHyperEdge to have some Extreme&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Extreme SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Extreme SuperHyperGraph $ESHG:(V,E),$ a Extreme SuperHyperVertex, titled its Extreme SuperHyperNeighbor,&nbsp; to that Extreme SuperHyperVertex in the Extreme SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Extreme procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Extreme SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Extreme SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Extreme SuperHyperNeighborhood. Thus the obvious Extreme R-Clique-Decompositions,&nbsp; $V_{ESHE}$ is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Clique-Decompositions,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Extreme SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Extreme SuperHyperVertices does forms any kind of Extreme pairs are titled&nbsp;&nbsp; \underline{Extreme SuperHyperNeighbors} in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Extreme SuperHyperCardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Extreme SuperHyperEdge to have some Extreme SuperHyperVertices uniquely. Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Any Extreme R-Clique-Decompositions only contains all interior Extreme SuperHyperVertices and all exterior Extreme SuperHyperVertices from the unique Extreme SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Extreme SuperHyperNeighbors in and there&#39;s all&nbsp; Extreme SuperHyperNeighborhoods in with no exception minus all&nbsp; Extreme SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Extreme SuperHyperNeighborhoods and Extreme SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Decompositions, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Extreme type-SuperHyperSet of the Extreme Clique-Decompositions. &nbsp;The Extreme SuperHyperSet of Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Extreme type-SuperHyperSet of the Extreme Clique-Decompositions. The Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Extreme Clique-Decompositions}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Extreme SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Clique-Decompositions is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Clique-Decompositions is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Extreme SuperHyperVertices. But the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Decompositions \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Decompositions. Since the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Extreme Clique-Decompositions $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Clique-Decompositions \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Clique-Decompositions}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There aren&#39;t&nbsp; only less than three Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Extreme Clique-Decompositions, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Clique-Decompositions, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Extreme SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; Clique-Decompositions&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme Clique-Decompositions}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}+z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Decompositions. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Decompositions taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}+z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Decompositions taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Decompositions. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}++z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Decompositions taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Decompositions. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. The unique embedded SuperHyperClique-Decompositions proposes some longest SuperHyperClique-Decompositions excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperClique-Decompositions in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Decompositions,&nbsp; Extreme SuperHyperClique-Decompositions, and the Extreme SuperHyperClique-Decompositions, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperClique-Decompositions is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperClique-Decompositions. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperClique-Decompositions=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Decompositions of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Decompositions \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperClique-Decompositions.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperClique-Decompositions and SuperHyperClique-Decompositions coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperClique-Decompositions if and only if it&#39;s a SuperHyperClique-Decompositions. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Decompositions if and only if it&#39;s a longest SuperHyperClique-Decompositions. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Decompositions is its SuperHyperClique-Decompositions and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperClique-Decompositions is its SuperHyperClique-Decompositions and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Decompositions/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Decompositions/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] the SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperClique-Decompositions/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Decompositions set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Decompositions. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Decompositions. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Decompositions. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperClique-Decompositions. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions or the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Decompositions} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperClique-Decompositions. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperClique-Decompositions} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperClique-Decompositions. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Decompositions and the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Decompositions and the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Decompositions and the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Decompositions and the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Decompositions, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Decompositions. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Decompositions, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Decompositions and the Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Decompositions}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperClique-Decompositions}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#194 Article&rdquo; Henry Garrett, &ldquo;New Ideas On Super Stale By Hyper Stalk Of Stable-Cut In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.20170.24000). @ResearchGate: https://www.researchgate.net/publication/369214553 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/98524637 &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas On Super Stale By Hyper Stalk Of Stable-Cut In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperStable-Cut). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Stable-Cut pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperStable-Cut if the following expression is called Neutrosophic e-SuperHyperStable-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; E&#39; \text{is Stable}; \end{eqnarray*} &nbsp;Neutrosophic re-SuperHyperStable-Cut if the following expression is called Neutrosophic e-SuperHyperStable-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; E&#39; \text{is Stable}; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperStable-Cut&nbsp; if the following expression is called Neutrosophic v-SuperHyperStable-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; V&#39; \text{is Stable}; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperStable-Cut if the following expression is called Neutrosophic v-SuperHyperStable-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; V&#39; \text{is Stable}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperStable-Cut if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut. ((Neutrosophic) SuperHyperStable-Cut). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperStable-Cut if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; a Neutrosophic SuperHyperStable-Cut if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; an Extreme SuperHyperStable-Cut SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperStable-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperStable-Cut if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; a Neutrosophic V-SuperHyperStable-Cut if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; an Extreme V-SuperHyperStable-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperStable-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperStable-Cut &nbsp;and Neutrosophic SuperHyperStable-Cut. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperStable-Cut is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperStable-Cut is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperStable-Cut . Since there&#39;s more ways to get type-results to make a SuperHyperStable-Cut &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperStable-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperStable-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperStable-Cut . It&#39;s redefined a Neutrosophic SuperHyperStable-Cut &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperStable-Cut . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperStable-Cut until the SuperHyperStable-Cut, then it&#39;s officially called a ``SuperHyperStable-Cut&#39;&#39; but otherwise, it isn&#39;t a SuperHyperStable-Cut . There are some instances about the clarifications for the main definition titled a ``SuperHyperStable-Cut &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperStable-Cut . For the sake of having a Neutrosophic SuperHyperStable-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperStable-Cut&#39;&#39; and a ``Neutrosophic SuperHyperStable-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperStable-Cut &nbsp;are redefined to a ``Neutrosophic SuperHyperStable-Cut&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperStable-Cut &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperStable-Cut&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperStable-Cut&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperStable-Cut &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperStable-Cut .] SuperHyperStable-Cut . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperStable-Cut if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperStable-Cut &nbsp;or the strongest SuperHyperStable-Cut &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperStable-Cut, called SuperHyperStable-Cut, and the strongest SuperHyperStable-Cut, called Neutrosophic SuperHyperStable-Cut, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperStable-Cut. There isn&#39;t any formation of any SuperHyperStable-Cut but literarily, it&#39;s the deformation of any SuperHyperStable-Cut. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperStable-Cut theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperStable-Cut, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Extreme SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Extreme SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperStable-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath (-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperStable-Cut or the Extreme&nbsp;&nbsp; SuperHyperStable-Cut in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperStable-Cut. There isn&#39;t any formation of any SuperHyperStable-Cut but literarily, it&#39;s the deformation of any SuperHyperStable-Cut. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperStable-Cut&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperStable-Cut&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperStable-Cut&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperStable-Cut&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Extreme SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperStable-Cut and Extreme&nbsp;&nbsp; SuperHyperStable-Cut, are figured out in sections ``&nbsp; SuperHyperStable-Cut&#39;&#39; and ``Extreme&nbsp;&nbsp; SuperHyperStable-Cut&#39;&#39;. In the sense of tackling on getting results and in Stable-Cut to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperStable-Cut&#39;&#39;, ``Extreme&nbsp;&nbsp; SuperHyperStable-Cut&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Extreme SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperStable-Cut&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Stable-Cut of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Stable-Cut of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperStable-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperStable-Cut} if the following expression is called \textbf{Neutrosophic e-SuperHyperStable-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; E&#39; \text{is Stable}; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperStable-Cut} if the following expression is called \textbf{Neutrosophic re-SuperHyperStable-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; E&#39; \text{is Stable}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperStable-Cut} if the following expression is called \textbf{Neutrosophic v-SuperHyperStable-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; V&#39; \text{is Stable}; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperStable-Cut} f the following expression is called \textbf{Neutrosophic v-SuperHyperStable-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; V&#39; \text{is Stable}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperStable-Cut} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperStable-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperStable-Cut} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperStable-Cut} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperStable-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperStable-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperStable-Cut} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperStable-Cut} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperStable-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperStable-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperStable-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperStable-Cut, Neutrosophic re-SuperHyperStable-Cut, Neutrosophic v-SuperHyperStable-Cut, and Neutrosophic rv-SuperHyperStable-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperStable-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperStable-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperStable-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperStable-Cut such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperStable-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperStable-Cut such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperStable-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperStable-Cut. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperStable-Cut more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperStable-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperStable-Cut&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperStable-Cut. It&#39;s redefined a \textbf{Neutrosophic SuperHyperStable-Cut} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Extreme SuperHyperStable-Cut But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Extreme event).\\ &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Any Extreme k-subset of $A$ of $V$ is called \textbf{Extreme k-event} and if $k=2,$ then Extreme subset of $A$ of $V$ is called \textbf{Extreme event}. The following expression is called \textbf{Extreme probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Extreme Independent).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. $s$ Extreme k-events $A_i,~i\in I$ is called \textbf{Extreme s-independent} if the following expression is called \textbf{Extreme s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Extreme k-events of $A$ and $B$ is called \textbf{Extreme independent}. The following expression is called \textbf{Extreme independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Extreme Variable).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Any k-function Stable-Cut like $E$ is called \textbf{Extreme k-Variable}. If $k=2$, then any 2-function Stable-Cut like $E$ is called \textbf{Extreme Variable}. \end{definition} The notion of independent on Extreme Variable is likewise. \begin{definition}(Extreme Expectation).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Expectation} if the following expression is called \textbf{Extreme Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Extreme Crossing).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. A Extreme number is called \textbf{Extreme Crossing} if the following expression is called \textbf{Extreme Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $m$ and $n$ propose special Stable-Cut. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Extreme&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Extreme independently with probability Stable-Cut $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Extreme number of SuperHyperVertices, $Y$ the Extreme number of SuperHyperEdges, and $Z$ the Extreme number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z \geq cr(H) \geq Y-3X.$ By linearity of Extreme Expectation, $$E(Z) \geq E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) \geq p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Extreme number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Extreme SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Extreme SuperHyperGraph has at least $kl$ SuperHyperEdges and Extreme crossing at most $l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Extreme Crossing Lemma, and again $l &lt; 32n^2/k^3.$ \end{proof} \begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Extreme number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{n-1}n_i = n$ and $k = \frac{1}{2}\sum{i=0}^{n-1}in_i.$ Now form a Extreme SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Extreme SuperHyperGraph $G$ with $e(G) \geq k-n.$ Now $cr(G)\leq n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) \geq cr(G) \geq {(k-n)}^3/64n^2$ by the Extreme Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $X$ be a nonnegative Extreme Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\}=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Stable-Cut $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Extreme SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Extreme Variable for this Extreme Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1\}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p\leq e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k \geq 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Extreme SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Extreme Variance).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. A Extreme k-Variable $E$ has a number is called \textbf{Extreme Variance} if the following expression is called \textbf{Extreme Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $X$ be a Extreme Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $X_n$ be a Extreme Variable in a probability Stable-Cut (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. The latter is straightforward. \end{proof} \begin{definition}(Extreme Threshold).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Extreme Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Extreme Balanced).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $F$ be a fixed Extreme SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Extreme SubSuperHyperGraph is called \textbf{Extreme Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. Let $F$ be a nonempty balanced Extreme SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Extreme SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Stable-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperStable-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}=3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperStable-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}=3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}}=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq1,2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i\neq1,5}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}}=2z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=1,4}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}=12z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_6,V_{15},V_9\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=4\times3\times4\times3z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^4},E_{{2j+23}_{{i=0}^4}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp; =2\times2z^{10}. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp; \\&amp;&amp; =\{V_{{2i+1}_{{i=0}^4},V_{{2j+11}_{{i=0}^4}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =2\times2z^{10}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_{{2i+1}_{{i=0}^4}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{{2i+1}_{{i=0}^4}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^3. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3\times4\times4z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^4}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =2z^{5}. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp; \\&amp;&amp; =\{V_{{2i+1}_{{i=0}^4}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp; =2z^{5}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^3. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3\times4\times4z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^3. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3\times3z^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=2,3,4,5,6}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=4,5,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^3. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3\times3z^2. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}}=\{V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}}= z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^2}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =2z^{3}. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp; \\&amp;&amp; =\{V_{{2i+2}_{{i=0}^1},V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =2z^{3}. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^2}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =2z^{3}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,V_3,V_{10},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =3\times4\times5z^4. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^2}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =2z^{3}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_{27},V_2,V_{10},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =7\times4\times4\times5z^4. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^2}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =2z^{3}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_{27},V_2,V_{10},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =7\times4\times4\times5z^4. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{{i=0}^5}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z^6. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;=\{V_{E_{{2i+1}_{{i=0}^5}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;=2z^6. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =az^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperStable-Cut, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+2}_{{i=0}^1}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,H_6,V_7,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =5\times4\times6\times5z^4. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Extreme SuperHyperGraphs Associated to the Extreme Notions of Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Stable-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Stable-Cut minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Stable-Cut, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Stable-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Stable-Cut is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Stable-Cut in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Stable-Cut. \end{proposition} \begin{proposition} &nbsp;Assume a simple Extreme SuperHyperGraph $ESHG:(V,E).$ Then the Extreme number of&nbsp; type-result-R-Stable-Cut has, the least Extreme cardinality, the lower sharp Extreme bound for Extreme cardinality, is the Extreme cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Extreme type-result-R-Stable-Cut with the least Extreme cardinality, the lower sharp Extreme bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Extreme type-result-Stable-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme type-result-Stable-Cut is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Stable-Cut since neither amount of Extreme SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Extreme number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Extreme SuperHyperSet of the Extreme SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices but the maximum Extreme cardinality indicates that these Extreme&nbsp; type-SuperHyperSets couldn&#39;t give us the Extreme lower bound in the term of Extreme sharpness. In other words, the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Extreme SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Extreme SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Extreme SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Stable-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Stable-Cut is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Extreme SuperHyperClasses of the connected loopless Extreme SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Stable-Cut. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Extreme SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Extreme structure of the Extreme R-Stable-Cut decorates the Extreme SuperHyperVertices don&#39;t have received any Extreme connections so as this Extreme style implies different versions of Extreme SuperHyperEdges with the maximum Extreme cardinality in the terms of Extreme SuperHyperVertices are spotlight. The lower Extreme bound is to have the maximum Extreme groups of Extreme SuperHyperVertices have perfect Extreme connections inside each of SuperHyperEdges and the outside of this Extreme SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Extreme SuperHyperGraph arising from its Extreme properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Extreme SuperHyperVertex in the targeted Extreme SuperHyperSet, then there&#39;s no Extreme connection. Furthermore, the Extreme existence of one Extreme SuperHyperVertex has no&nbsp; Extreme effect to talk about the Extreme R-Stable-Cut. Since at least two Extreme SuperHyperVertices involve to make a title in the Extreme background of the Extreme SuperHyperGraph. The Extreme SuperHyperGraph is obvious if it has no Extreme SuperHyperEdge but at least two Extreme SuperHyperVertices make the Extreme version of Extreme SuperHyperEdge. Thus in the Extreme setting of non-obvious Extreme SuperHyperGraph, there are at least one Extreme SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Extreme adjective for the initial Extreme SuperHyperGraph, induces there&#39;s no Extreme&nbsp; appearance of the loop Extreme version of the Extreme SuperHyperEdge and this Extreme SuperHyperGraph is said to be loopless. The Extreme adjective ``loop&#39;&#39; on the basic Extreme framework engages one Extreme SuperHyperVertex but it never happens in this Extreme setting. With these Extreme bases, on a Extreme SuperHyperGraph, there&#39;s at least one Extreme SuperHyperEdge thus there&#39;s at least a Extreme R-Stable-Cut has the Extreme cardinality of a Extreme SuperHyperEdge. Thus, a Extreme R-Stable-Cut has the Extreme cardinality at least a Extreme SuperHyperEdge. Assume a Extreme SuperHyperSet $V\setminus V\setminus \{z\}.$ This Extreme SuperHyperSet isn&#39;t a Extreme R-Stable-Cut since either the Extreme SuperHyperGraph is an obvious Extreme SuperHyperModel thus it never happens since there&#39;s no Extreme usage of this Extreme framework and even more there&#39;s no Extreme connection inside or the Extreme SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Extreme contradiction with the term ``Extreme R-Stable-Cut&#39;&#39; since the maximum Extreme cardinality never happens for this Extreme style of the Extreme SuperHyperSet and beyond that there&#39;s no Extreme connection inside as mentioned in first Extreme case in the forms of drawback for this selected Extreme SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Extreme case implies having the Extreme style of on-quasi-triangle Extreme style on the every Extreme elements of this Extreme SuperHyperSet. Precisely, the Extreme R-Stable-Cut is the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that some Extreme amount of the Extreme SuperHyperVertices are on-quasi-triangle Extreme style. The Extreme cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Extreme bound is up. Thus the minimum Extreme cardinality of the maximum Extreme cardinality ends up the Extreme discussion. The first Extreme term refers to the Extreme setting of the Extreme SuperHyperGraph but this key point is enough since there&#39;s a Extreme SuperHyperClass of a Extreme SuperHyperGraph has no on-quasi-triangle Extreme style amid some amount of its Extreme SuperHyperVertices. This Extreme setting of the Extreme SuperHyperModel proposes a Extreme SuperHyperSet has only some amount&nbsp; Extreme SuperHyperVertices from one Extreme SuperHyperEdge such that there&#39;s no Extreme amount of Extreme SuperHyperEdges more than one involving these some amount of these Extreme SuperHyperVertices. The Extreme cardinality of this Extreme SuperHyperSet is the maximum and the Extreme case is occurred in the minimum Extreme situation. To sum them up, the Extreme SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Extreme cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Extreme SuperHyperVertices such that there&#39;s distinct-covers-order-amount Extreme SuperHyperEdges for amount of Extreme SuperHyperVertices taken from the Extreme SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Extreme SuperHyperSet of the Extreme SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Extreme&nbsp; R-Stable-Cut for the Extreme SuperHyperGraph as used Extreme background in the Extreme terms of worst Extreme case and the common theme of the lower Extreme bound occurred in the specific Extreme SuperHyperClasses of the Extreme SuperHyperGraphs which are Extreme free-quasi-triangle. &nbsp; \\ Assume a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Extreme number of the Extreme SuperHyperVertices. Then every Extreme SuperHyperVertex has at least no Extreme SuperHyperEdge with others in common. Thus those Extreme SuperHyperVertices have the eligibles to be contained in a Extreme R-Stable-Cut. Those Extreme SuperHyperVertices are potentially included in a Extreme&nbsp; style-R-Stable-Cut. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Extreme SuperHyperVertices of a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Extreme&nbsp; SuperHyperVertices of the Extreme SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices and there&#39;s only and only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Extreme SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Extreme R-Stable-Cut is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Extreme R-Stable-Cut but with slightly differences in the maximum Extreme cardinality amid those Extreme type-SuperHyperSets of the Extreme SuperHyperVertices. Thus the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Extreme cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Extreme R-Stable-Cut. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Extreme SuperHyperVertices belong to the Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Stable-Cut}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Extreme R-Stable-Cut}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Extreme quasi-R-Stable-Cut where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Extreme intended SuperHyperVertices but in a Extreme Stable-Cut, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Extreme SuperHyperVertices, then the Extreme cardinality of the Extreme R-Stable-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Extreme cardinality of the Extreme R-Stable-Cut is at least the maximum Extreme number of Extreme SuperHyperVertices of the Extreme SuperHyperEdges with the maximum number of the Extreme SuperHyperEdges. In other words, the maximum number of the Extreme SuperHyperEdges contains the maximum Extreme number of Extreme SuperHyperVertices are renamed to Extreme Stable-Cut in some cases but the maximum number of the&nbsp; Extreme SuperHyperEdge with the maximum Extreme number of Extreme SuperHyperVertices, has the Extreme SuperHyperVertices are contained in a Extreme R-Stable-Cut. \\ The obvious SuperHyperGraph has no Extreme SuperHyperEdges. But the non-obvious Extreme SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Extreme optimal SuperHyperObject. It specially delivers some remarks on the Extreme SuperHyperSet of the Extreme SuperHyperVertices such that there&#39;s distinct amount of Extreme SuperHyperEdges for distinct amount of Extreme SuperHyperVertices up to all&nbsp; taken from that Extreme SuperHyperSet of the Extreme SuperHyperVertices but this Extreme SuperHyperSet of the Extreme SuperHyperVertices is either has the maximum Extreme SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Extreme SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Extreme SuperHyperEdge containing at least all Extreme SuperHyperVertices. Thus it forms a Extreme quasi-R-Stable-Cut where the Extreme completion of the Extreme incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Extreme embedded R-Stable-Cut. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Extreme SuperHyperCardinality and they&#39;re Extreme SuperHyperOptimal. The less than two distinct types of Extreme SuperHyperVertices are included in the minimum Extreme style of the embedded Extreme R-Stable-Cut. The interior types of the Extreme SuperHyperVertices are deciders. Since the Extreme number of SuperHyperNeighbors are only&nbsp; affected by the interior Extreme SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Extreme SuperHyperSet for any distinct types of Extreme SuperHyperVertices pose the Extreme R-Stable-Cut. Thus Extreme exterior SuperHyperVertices could be used only in one Extreme SuperHyperEdge and in Extreme SuperHyperRelation with the interior Extreme SuperHyperVertices in that&nbsp; Extreme SuperHyperEdge. In the embedded Extreme Stable-Cut, there&#39;s the usage of exterior Extreme SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Extreme SuperHyperVertex has no connection, inside. Thus, the Extreme SuperHyperSet of the Extreme SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Extreme R-Stable-Cut. The Extreme R-Stable-Cut with the exclusion of the exclusion of all&nbsp; Extreme SuperHyperVertices in one Extreme SuperHyperEdge and with other terms, the Extreme R-Stable-Cut with the inclusion of all Extreme SuperHyperVertices in one Extreme SuperHyperEdge, is a Extreme quasi-R-Stable-Cut. To sum them up, in a connected non-obvious Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Extreme SuperHyperVertices inside of any given Extreme quasi-R-Stable-Cut minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Extreme SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Extreme SuperHyperVertices in an&nbsp; Extreme quasi-R-Stable-Cut, minus all&nbsp; Extreme SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Extreme R-Stable-Cut has two titles. a Extreme quasi-R-Stable-Cut and its corresponded quasi-maximum Extreme R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Extreme number, there&#39;s a Extreme quasi-R-Stable-Cut with that quasi-maximum Extreme SuperHyperCardinality in the terms of the embedded Extreme SuperHyperGraph. If there&#39;s an embedded Extreme SuperHyperGraph, then the Extreme quasi-SuperHyperNotions lead us to take the collection of all the Extreme quasi-R-Stable-Cuts for all Extreme numbers less than its Extreme corresponded maximum number. The essence of the Extreme Stable-Cut ends up but this essence starts up in the terms of the Extreme quasi-R-Stable-Cut, again and more in the operations of collecting all the Extreme quasi-R-Stable-Cuts acted on the all possible used formations of the Extreme SuperHyperGraph to achieve one Extreme number. This Extreme number is\\ considered as the equivalence class for all corresponded quasi-R-Stable-Cuts. Let $z_{\text{Extreme Number}},S_{\text{Extreme SuperHyperSet}}$ and $G_{\text{Extreme Stable-Cut}}$ be a Extreme number, a Extreme SuperHyperSet and a Extreme Stable-Cut. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Extreme Number}}]_{\text{Extreme Class}}=\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Stable-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Extreme Stable-Cut is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Stable-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Extreme Stable-Cut. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Stable-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Extreme Stable-Cut poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Stable-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{S_{\text{Extreme SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Extreme SuperHyperSet}}=G_{\text{Extreme Stable-Cut}}, \\&amp;&amp;~|S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |S_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Extreme SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Extreme SuperHyperVertices such that any amount of its Extreme SuperHyperVertices are incident to a Extreme&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Extreme&nbsp; Quasi-Stable-Cut&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Extreme&nbsp; Quasi-Stable-Cut&#39;&#39; since ``Extreme Quasi-Stable-Cut&#39;&#39; happens ``Extreme Stable-Cut&#39;&#39; in a Extreme SuperHyperGraph as initial framework and background but ``Extreme SuperHyperNeighborhood&#39;&#39; may not happens ``Extreme Stable-Cut&#39;&#39; in a Extreme SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Extreme SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Extreme SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Extreme Quasi-Stable-Cut&#39;&#39;, and&nbsp; ``Extreme Stable-Cut&#39;&#39; are up. \\ Thus, let $z_{\text{Extreme Number}},N_{\text{Extreme SuperHyperNeighborhood}}$ and $G_{\text{Extreme Stable-Cut}}$ be a Extreme number, a Extreme SuperHyperNeighborhood and a Extreme Stable-Cut and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}\in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}= \\&amp;&amp; \cup_{z_{\text{Extreme Number}}}\{N_{\text{Extreme SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp;=z_{\text{Extreme Number}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperNeighborhood}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Extreme Number}}]_{\text{Extreme Class}}}z_{\text{Extreme Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Extreme Stable-Cut}}= \\&amp;&amp; \{N_{\text{Extreme SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Extreme Number}}}[z_{\text{Extreme Number}}]_{\text{Extreme Class}}~|~ \\&amp;&amp; |N_{\text{Extreme SuperHyperSet}}|_{\text{Extreme Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Stable-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperVertices is the simple Extreme type-SuperHyperSet of the Extreme R-Stable-Cut. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Extreme SuperHyperSet of Extreme SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Extreme type-SuperHyperSet of the Extreme R-Stable-Cut. The Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Extreme R-Stable-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge amid some Extreme SuperHyperVertices instead of all given by \underline{\textbf{Extreme Stable-Cut}} is related to the Extreme SuperHyperSet of the Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Extreme SuperHyperVertex \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Stable-Cut is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Stable-Cut is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Extreme SuperHyperVertex. But the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Stable-Cut \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of Extreme SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Stable-Cut. Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Extreme R-Stable-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Stable-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Stable-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme SuperHyperEdge for some amount Extreme&nbsp; SuperHyperVertices instead of all given by that Extreme type-SuperHyperSet called the&nbsp; Extreme Stable-Cut. There isn&#39;t&nbsp; only less than two Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Extreme R-Stable-Cut, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Stable-Cut, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Extreme SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; R-Stable-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme R-Stable-Cut}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Extreme SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Extreme free-triangle embedded SuperHyperModel and a Extreme on-triangle embedded SuperHyperModel but also it&#39;s a Extreme stable embedded SuperHyperModel. But all only non-obvious simple Extreme type-SuperHyperSets of the Extreme&nbsp; R-Stable-Cut amid those obvious simple Extreme type-SuperHyperSets of the Extreme Stable-Cut, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Extreme SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Extreme R-Stable-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Extreme&nbsp; R-Stable-Cut is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The all interior Extreme SuperHyperVertices belong to any Extreme quasi-R-Stable-Cut if for any of them, and any of other corresponded Extreme SuperHyperVertex, some interior Extreme SuperHyperVertices are mutually Extreme&nbsp; SuperHyperNeighbors with no Extreme exception at all minus&nbsp; all Extreme SuperHypeNeighbors to any amount of them. \\ Assume a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Extreme SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Extreme SuperHyperVertices $r.$ Consider all Extreme numbers of those Extreme SuperHyperVertices from that Extreme SuperHyperEdge excluding excluding more than $r$ distinct Extreme SuperHyperVertices, exclude to any given Extreme SuperHyperSet of the Extreme SuperHyperVertices. Consider there&#39;s a Extreme&nbsp; R-Stable-Cut with the least cardinality, the lower sharp Extreme bound for Extreme cardinality. Assume a connected Extreme SuperHyperGraph $ESHG:(V,E).$ The Extreme SuperHyperSet of the Extreme SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Extreme SuperHyperSet $S$ of&nbsp; the Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have&nbsp; some Extreme SuperHyperVertices uniquely but it isn&#39;t a Extreme R-Stable-Cut. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices such that there&#39;s a Extreme SuperHyperEdge to have some SuperHyperVertices uniquely. The Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Extreme cardinality of a Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices but it isn&#39;t a Extreme R-Stable-Cut. Since it \textbf{\underline{doesn&#39;t do}} the Extreme procedure such that such that there&#39;s a Extreme SuperHyperEdge to have some Extreme&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Extreme SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Extreme SuperHyperGraph $ESHG:(V,E),$ a Extreme SuperHyperVertex, titled its Extreme SuperHyperNeighbor,&nbsp; to that Extreme SuperHyperVertex in the Extreme SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Extreme procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Extreme SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Extreme SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Extreme SuperHyperNeighborhood. Thus the obvious Extreme R-Stable-Cut,&nbsp; $V_{ESHE}$ is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme R-Stable-Cut,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Extreme SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Extreme SuperHyperVertices does forms any kind of Extreme pairs are titled&nbsp;&nbsp; \underline{Extreme SuperHyperNeighbors} in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Since the Extreme SuperHyperSet of the Extreme SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Extreme SuperHyperCardinality}} of a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Extreme SuperHyperEdge to have some Extreme SuperHyperVertices uniquely. Thus, in a connected Extreme SuperHyperGraph $ESHG:(V,E).$ Any Extreme R-Stable-Cut only contains all interior Extreme SuperHyperVertices and all exterior Extreme SuperHyperVertices from the unique Extreme SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Extreme SuperHyperNeighbors in and there&#39;s all&nbsp; Extreme SuperHyperNeighborhoods in with no exception minus all&nbsp; Extreme SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Extreme SuperHyperNeighborhoods and Extreme SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Stable-Cut, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Extreme SuperHyperSet&nbsp; of Extreme&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Extreme type-SuperHyperSet of the Extreme Stable-Cut. &nbsp;The Extreme SuperHyperSet of Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Extreme type-SuperHyperSet of the Extreme Stable-Cut. The Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Extreme Stable-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is a Extreme&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Extreme cardinality}}&nbsp; of a Extreme SuperHyperSet $S$ of Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Extreme SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious&nbsp; Extreme Stable-Cut is up. The obvious simple Extreme type-SuperHyperSet called the&nbsp; Extreme Stable-Cut is a Extreme SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Extreme SuperHyperVertices. But the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Extreme SuperHyperSet. Thus the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Stable-Cut \underline{\textbf{is}} up. To sum them up, the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Stable-Cut. Since the Extreme SuperHyperSet of the Extreme SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Extreme Stable-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Extreme SuperHyperGraph $ESHG:(V,E)$ is the Extreme SuperHyperSet $S$ of Extreme SuperHyperVertices such that there&#39;s no a Extreme&nbsp; SuperHyperEdge for some&nbsp; Extreme SuperHyperVertices given by that Extreme type-SuperHyperSet&nbsp; called the&nbsp; Extreme Stable-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Extreme \underline{\textbf{ Stable-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Extreme cardinality}} of&nbsp; a Extreme SuperHyperSet $S$ of&nbsp; Extreme SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Extreme SuperHyperVertex of a Extreme SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Extreme SuperHyperEdge for all Extreme SuperHyperVertices. There aren&#39;t&nbsp; only less than three Extreme&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Extreme SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Extreme Stable-Cut, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Extreme type-SuperHyperSet of the&nbsp; Extreme Stable-Cut, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Extreme SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Extreme&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Extreme type-SuperHyperSet called the \begin{center} \underline{\textbf{``Extreme&nbsp; Stable-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Extreme type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Extreme Stable-Cut}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Extreme Quasi-Stable-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Extreme R-Quasi-Stable-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Extreme SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z^{\frac{|E_{NSHG}|}{2}}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=az^{\frac{|E_{NSHG}|}{2}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Extreme SuperHyperPath Associated to the Notions of&nbsp; Extreme SuperHyperStable-Cut in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z^{\frac{|E_{NSHG}|}{2}}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=az^{\frac{|E_{NSHG}|}{2}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Extreme SuperHyperCycle Associated to the Extreme Notions of&nbsp; Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=az^{\frac{|E_{NSHG}|}{2}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Extreme SuperHyperStar Associated to the Extreme Notions of&nbsp; Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\text{MATCHING SuperHyperEdges}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^{|\text{MATCHING SuperHyperEdges}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\text{One From Every MATCHING SuperHyperVertices} \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2bz^{|\text{One From Every MATCHING SuperHyperVertices|} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward. Then there&#39;s no at least one SuperHyperStable-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperStable-Cut could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperStable-Cut taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Extreme SuperHyperBipartite Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperStable-Cut in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\text{MATCHING SuperHyperEdges}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^{|\text{MATCHING SuperHyperEdges}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\text{One From Every MATCHING SuperHyperVertices} \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2bz^{|\text{One From Every MATCHING SuperHyperVertices|} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperStable-Cut taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperStable-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperStable-Cut could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Extreme SuperHyperStable-Cut in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Stable-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z^{\frac{|E_{NSHG}|}{2}}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme V-Stable-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_{{2i+1}_{2i+1=\lfloor |E_{NSHG}|\rfloor}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme V-Stable-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=az^{\frac{|E_{NSHG}|}{2}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperStable-Cut taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperStable-Cut. The latter is straightforward. Then there&#39;s at least one SuperHyperStable-Cut. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperStable-Cut could be applied. The unique embedded SuperHyperStable-Cut proposes some longest SuperHyperStable-Cut excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperStable-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Extreme SuperHyperWheel Extreme Associated to the Extreme Notions of&nbsp; Extreme SuperHyperStable-Cut in the Extreme Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperStable-Cut,&nbsp; Extreme SuperHyperStable-Cut, and the Extreme SuperHyperStable-Cut, some general results are introduced. \begin{remark} &nbsp;Let remind that the Extreme SuperHyperStable-Cut is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Extreme SuperHyperStable-Cut. Then &nbsp;\begin{eqnarray*} &amp;&amp; Extreme ~SuperHyperStable-Cut=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperStable-Cut of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperStable-Cut \\&amp;&amp; |_{Extreme cardinality amid those SuperHyperStable-Cut.}\} &nbsp; \end{eqnarray*} plus one Extreme SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Extreme SuperHyperStable-Cut and SuperHyperStable-Cut coincide. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Extreme SuperHyperStable-Cut if and only if it&#39;s a SuperHyperStable-Cut. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperStable-Cut if and only if it&#39;s a longest SuperHyperStable-Cut. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Extreme SuperHyperGraph on the same identical letter of the alphabet. Then its Extreme SuperHyperStable-Cut is its SuperHyperStable-Cut and reversely. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Extreme SuperHyperStable-Cut is its SuperHyperStable-Cut and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperStable-Cut isn&#39;t well-defined if and only if its SuperHyperStable-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperStable-Cut isn&#39;t well-defined if and only if its SuperHyperStable-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperStable-Cut isn&#39;t well-defined if and only if its SuperHyperStable-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Extreme SuperHyperGraph. Then its Extreme SuperHyperStable-Cut is well-defined if and only if its SuperHyperStable-Cut is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Extreme SuperHyperGraph. Then its Extreme SuperHyperStable-Cut is well-defined if and only if its SuperHyperStable-Cut is well-defined. \end{corollary} \begin{corollary} Assume a Extreme SuperHyperPath(-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Extreme SuperHyperStable-Cut is well-defined if and only if its SuperHyperStable-Cut is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Extreme SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStable-Cut/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperStable-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperStable-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStable-Cut/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperStable-Cut; &nbsp; \item[$(ii):$] the SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperStable-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperStable-Cut; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperStable-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Extreme number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Extreme number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Extreme SuperHyperGraph which is SuperHyperStable-Cut/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Extreme number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Extreme SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Extreme number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Extreme SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Extreme SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperStable-Cut, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperStable-Cut, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperStable-Cut set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperStable-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperStable-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperStable-Cut; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperStable-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Extreme SuperHyperStars with common Extreme SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperStable-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperStable-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperStable-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Extreme SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperStable-Cut for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperStable-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperStable-Cut, then $S$ is an s-SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperStable-Cut, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperStable-Cut, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperStable-Cut, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperStable-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Extreme SuperHyperGraph which is SuperHyperStable-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperStable-Cut. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Extreme Applications in Cancer&#39;s Extreme Recognition} The cancer is the Extreme disease but the Extreme model is going to figure out what&#39;s going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease. \\ In the following, some Extreme steps are Extreme devised on this disease. \begin{description} &nbsp;\item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function. &nbsp; \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it&#39;s called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Extreme SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Extreme Model)] &nbsp; There are some specific Extreme models, which are well-known and they&#39;ve got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Extreme SuperHyperPath(-/SuperHyperStable-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Extreme&nbsp;&nbsp; SuperHyperStable-Cut or the Extreme&nbsp;&nbsp; SuperHyperStable-Cut in those Extreme Extreme SuperHyperModels. &nbsp; \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as&nbsp; Extreme SuperHyperModel} &nbsp;\item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa21aa}, the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperStable-Cut} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Extreme Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Extreme SuperHyperBipartite is obtained. \\ The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa21aa}, is the Extreme SuperHyperStable-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Extreme Solution)] In the Extreme Figure \eqref{136NSHGaa22aa}, the Extreme SuperHyperMultipartite is Extreme highlighted and&nbsp; Extreme featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Extreme&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Extreme SuperHyperStable-Cut} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Extreme Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Extreme SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Extreme SuperHyperStable-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Extreme SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperStable-Cut and the Extreme&nbsp;&nbsp; SuperHyperStable-Cut are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperStable-Cut and the Extreme&nbsp;&nbsp; SuperHyperStable-Cut? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperStable-Cut and the Extreme&nbsp;&nbsp; SuperHyperStable-Cut? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperStable-Cut and the Extreme&nbsp;&nbsp; SuperHyperStable-Cut do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperStable-Cut, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperStable-Cut. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme&nbsp;&nbsp; SuperHyperStable-Cut, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperStable-Cut, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperStable-Cut and the Extreme&nbsp;&nbsp; SuperHyperStable-Cut. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperStable-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Extreme SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperStable-Cut}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Extreme&nbsp;&nbsp; SuperHyperStable-Cut}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperDuality).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperDuality, Extreme re-SuperHyperDuality, Extreme v-SuperHyperDuality, and Extreme rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperJoin).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperJoin, Extreme re-SuperHyperJoin, Extreme v-SuperHyperJoin, and Extreme rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperPerfect).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperPerfect, Extreme re-SuperHyperPerfect, Extreme v-SuperHyperPerfect, and Extreme rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Extreme Types of Extreme SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperTotal).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperTotal, Extreme re-SuperHyperTotal, Extreme v-SuperHyperTotal, and Extreme rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Extreme Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Extreme Types of Extreme SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Extreme e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Extreme re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Extreme v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Extreme rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Extreme) SuperHyperConnected).\\ &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Extreme SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Extreme SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality&nbsp; consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Extreme e-SuperHyperConnected, Extreme re-SuperHyperConnected, Extreme v-SuperHyperConnected, and Extreme rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Extreme SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of a Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Extreme SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Extreme Figures in every Extreme items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Extreme SuperHyperEdge and $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Extreme SuperHyperEdges but $E_4$ is a Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there&#39;s only one Extreme SuperHyperEdge, namely, $E_4.$ The Extreme SuperHyperVertex, $V_3$ is Extreme isolated means that there&#39;s no Extreme SuperHyperEdge has it as a Extreme endpoint. Thus the Extreme SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses. \begin{proposition} Assume a connected Extreme SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Extreme SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Extreme SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Extreme SuperHyperSet,&nbsp; in the Extreme SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Extreme SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Extreme SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, in the Extreme SuperHyperModel \eqref{136NSHG19a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Extreme SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Extreme SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the&nbsp; Extreme SuperHyperVertices of the connected Extreme SuperHyperStar $ESHS:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Extreme Figure \eqref{136NSHG21a}, the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite $ESHB:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG21a}, is the Extreme&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Extreme SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Extreme-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Extreme SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite $ESHM:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Extreme SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Extreme SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Extreme Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Extreme V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Extreme SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Extreme Figure \eqref{136NSHG23a}, the connected Extreme SuperHyperWheel $NSHW:(V,E),$ is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel $ESHW:(V,E),$ in the Extreme SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Extreme SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#193 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Neighbors As Hyper Nebbish On Super Nebulous&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.36475.59683). @ResearchGate: https://www.researchgate.net/publication/369196398 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Neighbors As Hyper Nebbish&nbsp; On Super Nebulous } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Neighbors). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Neighbors pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Neighbors if the following expression is called Neutrosophic e-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} &nbsp;Neutrosophic re-SuperHyperClique-Neighbors if the following expression is called Neutrosophic e-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Neighbors&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Neighbors if the following expression is called Neutrosophic v-SuperHyperClique-Neighbors criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors. ((Neutrosophic) SuperHyperClique-Neighbors). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; a Neutrosophic SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; an Extreme SuperHyperClique-Neighbors SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; a Neutrosophic V-SuperHyperClique-Neighbors if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; an Extreme V-SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Neighbors &nbsp;and Neutrosophic SuperHyperClique-Neighbors. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Neighbors is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Neighbors is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Neighbors . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Neighbors &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Neighbors &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Neighbors . It&#39;s redefined a Neutrosophic SuperHyperClique-Neighbors &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Neighbors . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Neighbors until the SuperHyperClique-Neighbors, then it&#39;s officially called a ``SuperHyperClique-Neighbors&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Neighbors . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Neighbors &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Neighbors . For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; and a ``Neutrosophic SuperHyperClique-Neighbors &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Neighbors &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Neighbors &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Neighbors &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Neighbors .] SuperHyperClique-Neighbors . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Neighbors if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Neighbors &nbsp;or the strongest SuperHyperClique-Neighbors &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Neighbors, called SuperHyperClique-Neighbors, and the strongest SuperHyperClique-Neighbors, called Neutrosophic SuperHyperClique-Neighbors, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Neighbors. There isn&#39;t any formation of any SuperHyperClique-Neighbors but literarily, it&#39;s the deformation of any SuperHyperClique-Neighbors. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Neighbors theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperClique-Neighbors, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Neighbors or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Neighbors. There isn&#39;t any formation of any SuperHyperClique-Neighbors but literarily, it&#39;s the deformation of any SuperHyperClique-Neighbors. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Neighbors and Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors, are figured out in sections ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39;. In the sense of tackling on getting results and in Clique-Neighbors to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Neighbors&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Neighbors&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Neighbors of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Neighbors of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a\in E&#39;: N(E_a) \text{is Clique}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Neighbors} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Neighbors} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Neighbors criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a\in V&#39;: N(V_a) \text{is Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Neighbors} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Neighbors; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Neighbors SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Neighbors, Neutrosophic re-SuperHyperClique-Neighbors, Neutrosophic v-SuperHyperClique-Neighbors, and Neutrosophic rv-SuperHyperClique-Neighbors and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Neighbors; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Neighbors).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Neighbors} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Neighbors such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Neighbors} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Neighbors such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Neighbors. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Neighbors more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Neighbors, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Neighbors&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Neighbors. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Neighbors} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperClique-Neighbors But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Any k-function Clique-Neighbors like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function Clique-Neighbors like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $m$ and $n$ propose special Clique-Neighbors. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability Clique-Neighbors $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Neighbors $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $X_n$ be a Neutrosophic Variable in a probability Clique-Neighbors (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Neighbors. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Neighbors. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}=\{V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_6,V_{15},V_9,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5_2z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,\ldots\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,\ldots\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =az. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_2,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =0z^0. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{i_{i=1,2,3}},V_{j_{j=4,5,6,7}},V_{k_{k=8,9,10,11}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =0z^0. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^{10}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_{i_{{i=1}^7}},V_{j{{j=8}^{11}}},V_{k{{k=1}^3}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=0z^0. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}=\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=2,3,4,5,6}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{E_i\}_{i=4,5,6,9,10}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=0z^0. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}=\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=0z^0. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}}=\{V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}}= 2z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; =0z^0. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}},V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+z^5+z^4+z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=23}^{29}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+z^6+z^5+z^4. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}}=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; &nbsp; &nbsp;&nbsp; =\{V_{i_{{i=8}^{17}}},V_{i_{{i=24}^{29}}},V_{i_{{i=18}^{22}}},V_{i_{{i=3}^{5}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^9+2z^5+z^4. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_{i_{V_i\in E_8,~i\neq7,8}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =az^{6}+\ldots+z^3. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =az^b+\ldots+cz^b. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=10z^9. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Neighbors, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{H_6,O_6,E_6,C_6,\ldots,\text{INTERNAL SuperHyperVERTICES}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =11z^{11}+4z^9+5z^8+4z^5. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Neighbors minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Neighbors, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Neighbors is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Neighbors is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Neighbors in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Neighbors. \end{proposition} \begin{proposition} &nbsp;Assume a simple Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then the Neutrosophic number of&nbsp; type-result-R-Clique-Neighbors has, the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality, is the Neutrosophic cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Neutrosophic type-result-R-Clique-Neighbors with the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Neutrosophic type-result-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic type-result-Clique-Neighbors is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Neighbors since neither amount of Neutrosophic SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Neutrosophic number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices but the maximum Neutrosophic cardinality indicates that these Neutrosophic&nbsp; type-SuperHyperSets couldn&#39;t give us the Neutrosophic lower bound in the term of Neutrosophic sharpness. In other words, the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Neutrosophic SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Neutrosophic SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Neutrosophic SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Neighbors is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Neutrosophic SuperHyperClasses of the connected loopless Neutrosophic SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Neighbors. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Neutrosophic SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Neutrosophic structure of the Neutrosophic R-Clique-Neighbors decorates the Neutrosophic SuperHyperVertices don&#39;t have received any Neutrosophic connections so as this Neutrosophic style implies different versions of Neutrosophic SuperHyperEdges with the maximum Neutrosophic cardinality in the terms of Neutrosophic SuperHyperVertices are spotlight. The lower Neutrosophic bound is to have the maximum Neutrosophic groups of Neutrosophic SuperHyperVertices have perfect Neutrosophic connections inside each of SuperHyperEdges and the outside of this Neutrosophic SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Neutrosophic SuperHyperGraph arising from its Neutrosophic properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Neutrosophic SuperHyperVertex in the targeted Neutrosophic SuperHyperSet, then there&#39;s no Neutrosophic connection. Furthermore, the Neutrosophic existence of one Neutrosophic SuperHyperVertex has no&nbsp; Neutrosophic effect to talk about the Neutrosophic R-Clique-Neighbors. Since at least two Neutrosophic SuperHyperVertices involve to make a title in the Neutrosophic background of the Neutrosophic SuperHyperGraph. The Neutrosophic SuperHyperGraph is obvious if it has no Neutrosophic SuperHyperEdge but at least two Neutrosophic SuperHyperVertices make the Neutrosophic version of Neutrosophic SuperHyperEdge. Thus in the Neutrosophic setting of non-obvious Neutrosophic SuperHyperGraph, there are at least one Neutrosophic SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Neutrosophic adjective for the initial Neutrosophic SuperHyperGraph, induces there&#39;s no Neutrosophic&nbsp; appearance of the loop Neutrosophic version of the Neutrosophic SuperHyperEdge and this Neutrosophic SuperHyperGraph is said to be loopless. The Neutrosophic adjective ``loop&#39;&#39; on the basic Neutrosophic framework engages one Neutrosophic SuperHyperVertex but it never happens in this Neutrosophic setting. With these Neutrosophic bases, on a Neutrosophic SuperHyperGraph, there&#39;s at least one Neutrosophic SuperHyperEdge thus there&#39;s at least a Neutrosophic R-Clique-Neighbors has the Neutrosophic cardinality of a Neutrosophic SuperHyperEdge. Thus, a Neutrosophic R-Clique-Neighbors has the Neutrosophic cardinality at least a Neutrosophic SuperHyperEdge. Assume a Neutrosophic SuperHyperSet $V\setminus V\setminus \{z\}.$ This Neutrosophic SuperHyperSet isn&#39;t a Neutrosophic R-Clique-Neighbors since either the Neutrosophic SuperHyperGraph is an obvious Neutrosophic SuperHyperModel thus it never happens since there&#39;s no Neutrosophic usage of this Neutrosophic framework and even more there&#39;s no Neutrosophic connection inside or the Neutrosophic SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Neutrosophic contradiction with the term ``Neutrosophic R-Clique-Neighbors&#39;&#39; since the maximum Neutrosophic cardinality never happens for this Neutrosophic style of the Neutrosophic SuperHyperSet and beyond that there&#39;s no Neutrosophic connection inside as mentioned in first Neutrosophic case in the forms of drawback for this selected Neutrosophic SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Neutrosophic case implies having the Neutrosophic style of on-quasi-triangle Neutrosophic style on the every Neutrosophic elements of this Neutrosophic SuperHyperSet. Precisely, the Neutrosophic R-Clique-Neighbors is the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that some Neutrosophic amount of the Neutrosophic SuperHyperVertices are on-quasi-triangle Neutrosophic style. The Neutrosophic cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Neutrosophic bound is up. Thus the minimum Neutrosophic cardinality of the maximum Neutrosophic cardinality ends up the Neutrosophic discussion. The first Neutrosophic term refers to the Neutrosophic setting of the Neutrosophic SuperHyperGraph but this key point is enough since there&#39;s a Neutrosophic SuperHyperClass of a Neutrosophic SuperHyperGraph has no on-quasi-triangle Neutrosophic style amid some amount of its Neutrosophic SuperHyperVertices. This Neutrosophic setting of the Neutrosophic SuperHyperModel proposes a Neutrosophic SuperHyperSet has only some amount&nbsp; Neutrosophic SuperHyperVertices from one Neutrosophic SuperHyperEdge such that there&#39;s no Neutrosophic amount of Neutrosophic SuperHyperEdges more than one involving these some amount of these Neutrosophic SuperHyperVertices. The Neutrosophic cardinality of this Neutrosophic SuperHyperSet is the maximum and the Neutrosophic case is occurred in the minimum Neutrosophic situation. To sum them up, the Neutrosophic SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Neutrosophic cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Neutrosophic SuperHyperVertices such that there&#39;s distinct-covers-order-amount Neutrosophic SuperHyperEdges for amount of Neutrosophic SuperHyperVertices taken from the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Neutrosophic&nbsp; R-Clique-Neighbors for the Neutrosophic SuperHyperGraph as used Neutrosophic background in the Neutrosophic terms of worst Neutrosophic case and the common theme of the lower Neutrosophic bound occurred in the specific Neutrosophic SuperHyperClasses of the Neutrosophic SuperHyperGraphs which are Neutrosophic free-quasi-triangle. &nbsp; \\ Assume a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Neutrosophic number of the Neutrosophic SuperHyperVertices. Then every Neutrosophic SuperHyperVertex has at least no Neutrosophic SuperHyperEdge with others in common. Thus those Neutrosophic SuperHyperVertices have the eligibles to be contained in a Neutrosophic R-Clique-Neighbors. Those Neutrosophic SuperHyperVertices are potentially included in a Neutrosophic&nbsp; style-R-Clique-Neighbors. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Neutrosophic&nbsp; SuperHyperVertices of the Neutrosophic SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices and there&#39;s only and only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Neutrosophic SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Neutrosophic R-Clique-Neighbors is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Neutrosophic R-Clique-Neighbors but with slightly differences in the maximum Neutrosophic cardinality amid those Neutrosophic type-SuperHyperSets of the Neutrosophic SuperHyperVertices. Thus the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Neutrosophic cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Neutrosophic R-Clique-Neighbors. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices belong to the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Neighbors}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Neighbors}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Neutrosophic quasi-R-Clique-Neighbors where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Neutrosophic intended SuperHyperVertices but in a Neutrosophic Clique-Neighbors, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Neighbors is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Neighbors is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Neighbors in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Neighbors. \\ The obvious SuperHyperGraph has no Neutrosophic SuperHyperEdges. But the non-obvious Neutrosophic SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Neutrosophic optimal SuperHyperObject. It specially delivers some remarks on the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that there&#39;s distinct amount of Neutrosophic SuperHyperEdges for distinct amount of Neutrosophic SuperHyperVertices up to all&nbsp; taken from that Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices but this Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices is either has the maximum Neutrosophic SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Neutrosophic SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Neutrosophic SuperHyperEdge containing at least all Neutrosophic SuperHyperVertices. Thus it forms a Neutrosophic quasi-R-Clique-Neighbors where the Neutrosophic completion of the Neutrosophic incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Neutrosophic embedded R-Clique-Neighbors. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Neutrosophic SuperHyperCardinality and they&#39;re Neutrosophic SuperHyperOptimal. The less than two distinct types of Neutrosophic SuperHyperVertices are included in the minimum Neutrosophic style of the embedded Neutrosophic R-Clique-Neighbors. The interior types of the Neutrosophic SuperHyperVertices are deciders. Since the Neutrosophic number of SuperHyperNeighbors are only&nbsp; affected by the interior Neutrosophic SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Neutrosophic SuperHyperSet for any distinct types of Neutrosophic SuperHyperVertices pose the Neutrosophic R-Clique-Neighbors. Thus Neutrosophic exterior SuperHyperVertices could be used only in one Neutrosophic SuperHyperEdge and in Neutrosophic SuperHyperRelation with the interior Neutrosophic SuperHyperVertices in that&nbsp; Neutrosophic SuperHyperEdge. In the embedded Neutrosophic Clique-Neighbors, there&#39;s the usage of exterior Neutrosophic SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Neutrosophic SuperHyperVertex has no connection, inside. Thus, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Neutrosophic R-Clique-Neighbors. The Neutrosophic R-Clique-Neighbors with the exclusion of the exclusion of all&nbsp; Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge and with other terms, the Neutrosophic R-Clique-Neighbors with the inclusion of all Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge, is a Neutrosophic quasi-R-Clique-Neighbors. To sum them up, in a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Neighbors minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Neighbors, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Neutrosophic R-Clique-Neighbors has two titles. a Neutrosophic quasi-R-Clique-Neighbors and its corresponded quasi-maximum Neutrosophic R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Neutrosophic number, there&#39;s a Neutrosophic quasi-R-Clique-Neighbors with that quasi-maximum Neutrosophic SuperHyperCardinality in the terms of the embedded Neutrosophic SuperHyperGraph. If there&#39;s an embedded Neutrosophic SuperHyperGraph, then the Neutrosophic quasi-SuperHyperNotions lead us to take the collection of all the Neutrosophic quasi-R-Clique-Neighborss for all Neutrosophic numbers less than its Neutrosophic corresponded maximum number. The essence of the Neutrosophic Clique-Neighbors ends up but this essence starts up in the terms of the Neutrosophic quasi-R-Clique-Neighbors, again and more in the operations of collecting all the Neutrosophic quasi-R-Clique-Neighborss acted on the all possible used formations of the Neutrosophic SuperHyperGraph to achieve one Neutrosophic number. This Neutrosophic number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Neighborss. Let $z_{\text{Neutrosophic Number}},S_{\text{Neutrosophic SuperHyperSet}}$ and $G_{\text{Neutrosophic Clique-Neighbors}}$ be a Neutrosophic number, a Neutrosophic SuperHyperSet and a Neutrosophic Clique-Neighbors. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}=\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Neutrosophic Clique-Neighbors is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Neutrosophic Clique-Neighbors. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Neutrosophic Clique-Neighbors poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Neighbors}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Neutrosophic SuperHyperVertices such that any amount of its Neutrosophic SuperHyperVertices are incident to a Neutrosophic&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Neutrosophic&nbsp; Quasi-Clique-Neighbors&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Neutrosophic&nbsp; Quasi-Clique-Neighbors&#39;&#39; since ``Neutrosophic Quasi-Clique-Neighbors&#39;&#39; happens ``Neutrosophic Clique-Neighbors&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and background but ``Neutrosophic SuperHyperNeighborhood&#39;&#39; may not happens ``Neutrosophic Clique-Neighbors&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Neutrosophic SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Neutrosophic Quasi-Clique-Neighbors&#39;&#39;, and&nbsp; ``Neutrosophic Clique-Neighbors&#39;&#39; are up. \\ Thus, let $z_{\text{Neutrosophic Number}},N_{\text{Neutrosophic SuperHyperNeighborhood}}$ and $G_{\text{Neutrosophic Clique-Neighbors}}$ be a Neutrosophic number, a Neutrosophic SuperHyperNeighborhood and a Neutrosophic Clique-Neighbors and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Neighbors}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperVertices is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Neighbors. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Neighbors. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Neutrosophic R-Clique-Neighbors}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge amid some Neutrosophic SuperHyperVertices instead of all given by \underline{\textbf{Neutrosophic Clique-Neighbors}} is related to the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Neighbors is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Neighbors is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex. But the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Neighbors \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Neighbors. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Neutrosophic R-Clique-Neighbors $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Neighbors \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Neighbors}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic SuperHyperEdge for some amount Neutrosophic&nbsp; SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Neighbors. There isn&#39;t&nbsp; only less than two Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Neutrosophic R-Clique-Neighbors, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Neighbors, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Neutrosophic SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; R-Clique-Neighbors&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic R-Clique-Neighbors}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Neutrosophic free-triangle embedded SuperHyperModel and a Neutrosophic on-triangle embedded SuperHyperModel but also it&#39;s a Neutrosophic stable embedded SuperHyperModel. But all only non-obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic&nbsp; R-Clique-Neighbors amid those obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic Clique-Neighbors, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Neutrosophic R-Clique-Neighbors. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic&nbsp; R-Clique-Neighbors is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Neighbors if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Neutrosophic SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Neutrosophic SuperHyperVertices $r.$ Consider all Neutrosophic numbers of those Neutrosophic SuperHyperVertices from that Neutrosophic SuperHyperEdge excluding excluding more than $r$ distinct Neutrosophic SuperHyperVertices, exclude to any given Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices. Consider there&#39;s a Neutrosophic&nbsp; R-Clique-Neighbors with the least cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality. Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Neutrosophic SuperHyperSet $S$ of&nbsp; the Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have&nbsp; some Neutrosophic SuperHyperVertices uniquely but it isn&#39;t a Neutrosophic R-Clique-Neighbors. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have some SuperHyperVertices uniquely. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Neutrosophic cardinality of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices but it isn&#39;t a Neutrosophic R-Clique-Neighbors. Since it \textbf{\underline{doesn&#39;t do}} the Neutrosophic procedure such that such that there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Neutrosophic SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Neutrosophic SuperHyperGraph $ESHG:(V,E),$ a Neutrosophic SuperHyperVertex, titled its Neutrosophic SuperHyperNeighbor,&nbsp; to that Neutrosophic SuperHyperVertex in the Neutrosophic SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Neutrosophic procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Neutrosophic SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Neutrosophic SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Neutrosophic SuperHyperNeighborhood. Thus the obvious Neutrosophic R-Clique-Neighbors,&nbsp; $V_{ESHE}$ is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Neighbors,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Neutrosophic SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Neutrosophic SuperHyperVertices does forms any kind of Neutrosophic pairs are titled&nbsp;&nbsp; \underline{Neutrosophic SuperHyperNeighbors} in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Neutrosophic SuperHyperCardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic SuperHyperVertices uniquely. Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Any Neutrosophic R-Clique-Neighbors only contains all interior Neutrosophic SuperHyperVertices and all exterior Neutrosophic SuperHyperVertices from the unique Neutrosophic SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Neutrosophic SuperHyperNeighbors in and there&#39;s all&nbsp; Neutrosophic SuperHyperNeighborhoods in with no exception minus all&nbsp; Neutrosophic SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Neutrosophic SuperHyperNeighborhoods and Neutrosophic SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Neighbors, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Neighbors. &nbsp;The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Neighbors. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Neutrosophic Clique-Neighbors}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Neighbors is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Neighbors is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices. But the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Neighbors \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Neighbors. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Neutrosophic Clique-Neighbors $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Neighbors \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Neighbors}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There aren&#39;t&nbsp; only less than three Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Neutrosophic Clique-Neighbors, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Neighbors, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Neutrosophic SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; Clique-Neighbors&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic Clique-Neighbors}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Neighbors SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Neighbors SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Neighbors. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Neighbors taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Neighbors taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Neighbors. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Neighbors SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=0z^0. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Neighbors}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{INTERNAL}_i_{{V^{INTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}},\ldots,\text{INTERNAL SuperHyperVERTICES}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Neighbors SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+z^{\min |E_a|_{E_a\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Neighbors taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Neighbors. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Neighbors. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Neighbors could be applied. The unique embedded SuperHyperClique-Neighbors proposes some longest SuperHyperClique-Neighbors excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperClique-Neighbors. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Neighbors in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Neighbors,&nbsp; Neutrosophic SuperHyperClique-Neighbors, and the Neutrosophic SuperHyperClique-Neighbors, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperClique-Neighbors is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperClique-Neighbors. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperClique-Neighbors=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Neighbors of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Neighbors \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperClique-Neighbors.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperClique-Neighbors and SuperHyperClique-Neighbors coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperClique-Neighbors if and only if it&#39;s a SuperHyperClique-Neighbors. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Neighbors if and only if it&#39;s a longest SuperHyperClique-Neighbors. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Neighbors is its SuperHyperClique-Neighbors and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Neighbors is its SuperHyperClique-Neighbors and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Neighbors isn&#39;t well-defined if and only if its SuperHyperClique-Neighbors isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Neighbors is well-defined if and only if its SuperHyperClique-Neighbors is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Neighbors/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Neighbors; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Neighbors; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Neighbors/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] the SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperClique-Neighbors/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Neighbors set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Neighbors. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Neighbors. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Neighbors; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Neighbors for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Neighbors, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Neighbors. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Neighbors. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Neighbors. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Neighbors, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Neighbors} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperClique-Neighbors. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Neighbors} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperClique-Neighbors. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Neighbors and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Neighbors and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Neighbors and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Neighbors and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Neighbors, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Neighbors. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Neighbors, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Neighbors and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Neighbors&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Neighbors}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperClique-Neighbors}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By List-Coloring As Hyper List On Super Lisle } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperList-Coloring). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a List-Coloring pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperList-Coloring if the following expression is called Neutrosophic e-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*}&nbsp; Neutrosophic re-SuperHyperList-Coloring if the following expression is called Neutrosophic e-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperList-Coloring&nbsp; if the following expression is called Neutrosophic v-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperList-Coloring if the following expression is called Neutrosophic v-SuperHyperList-Coloring criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring. ((Neutrosophic) SuperHyperList-Coloring). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; a Neutrosophic SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; an Extreme SuperHyperList-Coloring SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; a Neutrosophic V-SuperHyperList-Coloring if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; an Extreme V-SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperList-Coloring &nbsp;and Neutrosophic SuperHyperList-Coloring. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperList-Coloring is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperList-Coloring is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperList-Coloring . Since there&#39;s more ways to get type-results to make a SuperHyperList-Coloring &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperList-Coloring &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperList-Coloring . It&#39;s redefined a Neutrosophic SuperHyperList-Coloring &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperList-Coloring . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperList-Coloring until the SuperHyperList-Coloring, then it&#39;s officially called a ``SuperHyperList-Coloring&#39;&#39; but otherwise, it isn&#39;t a SuperHyperList-Coloring . There are some instances about the clarifications for the main definition titled a ``SuperHyperList-Coloring &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperList-Coloring . For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; and a ``Neutrosophic SuperHyperList-Coloring &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperList-Coloring &nbsp;are redefined to a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperList-Coloring &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperList-Coloring&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperList-Coloring&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperList-Coloring &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperList-Coloring .] SuperHyperList-Coloring . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperList-Coloring if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperList-Coloring &nbsp;or the strongest SuperHyperList-Coloring &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperList-Coloring, called SuperHyperList-Coloring, and the strongest SuperHyperList-Coloring, called Neutrosophic SuperHyperList-Coloring, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperList-Coloring. There isn&#39;t any formation of any SuperHyperList-Coloring but literarily, it&#39;s the deformation of any SuperHyperList-Coloring. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperList-Coloring theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperList-Coloring, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperList-Coloring&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperList-Coloring or the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperList-Coloring. There isn&#39;t any formation of any SuperHyperList-Coloring but literarily, it&#39;s the deformation of any SuperHyperList-Coloring. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperList-Coloring&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperList-Coloring and Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring, are figured out in sections ``&nbsp; SuperHyperList-Coloring&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39;. In the sense of tackling on getting results and in List-Coloring to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperList-Coloring&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperList-Coloring&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a List-Coloring of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a List-Coloring of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic e-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic re-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E\in E_{NSHG}, E\sim i,~i\in \Bbb N \\&amp;&amp; \forall E_a\in E_{NSHG}, \exists E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim i,E_b\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperList-Coloring} if the following expression is called \textbf{Neutrosophic v-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperList-Coloring} f the following expression is called \textbf{Neutrosophic v-SuperHyperList-Coloring criteria} holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall V\in V_{NSHG}, V\sim i,~i\in \Bbb N \\&amp;&amp; \forall V_a\in V_{NSHG}, \exists V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim i,V_j\sim j,~i\neq j~i,j\in \Bbb N; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperList-Coloring} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperList-Coloring; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperList-Coloring SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperList-Coloring, Neutrosophic re-SuperHyperList-Coloring, Neutrosophic v-SuperHyperList-Coloring, and Neutrosophic rv-SuperHyperList-Coloring and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperList-Coloring; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperList-Coloring).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperList-Coloring} is a Neutrosophic kind of Neutrosophic SuperHyperList-Coloring such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperList-Coloring} is a Neutrosophic kind of Neutrosophic SuperHyperList-Coloring such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperList-Coloring. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperList-Coloring more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperList-Coloring, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperList-Coloring&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperList-Coloring. It&#39;s redefined a \textbf{Neutrosophic SuperHyperList-Coloring} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperList-Coloring But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Any k-function List-Coloring like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function List-Coloring like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $m$ and $n$ propose special List-Coloring. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability List-Coloring $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability List-Coloring $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $X_n$ be a Neutrosophic Variable in a probability List-Coloring (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability List-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperList-Coloring. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperList-Coloring. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=2z. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_1,V_2,V_3,N,F\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =(\text{Seven Choose Four})z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=4z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i,V_{13}\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{13},V_i\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =2z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_i,V_{13}\}_{i=1}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =5z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=5z^2. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=z^5. &nbsp;\end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=6z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}}= 2z^3. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; =2z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}}=11z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{V_i\in E_2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z^{7}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{10}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_i\}_{V_i\in E_6}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10z^{|E_6|}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperList-Coloring, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =4z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{M_6,L_6,F,V_3,V_2,H_6,O_6,E_6,C_6,Z_5,W_5,V_{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{12}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-List-Coloring if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-List-Coloring minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-List-Coloring, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-List-Coloring is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-List-Coloring is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic List-Coloring in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-List-Coloring. \end{proposition} \begin{proposition} &nbsp;Assume a simple Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then the Neutrosophic number of&nbsp; type-result-R-List-Coloring has, the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality, is the Neutrosophic cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Neutrosophic type-result-R-List-Coloring with the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Neutrosophic type-result-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic type-result-List-Coloring is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-List-Coloring since neither amount of Neutrosophic SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Neutrosophic number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices but the maximum Neutrosophic cardinality indicates that these Neutrosophic&nbsp; type-SuperHyperSets couldn&#39;t give us the Neutrosophic lower bound in the term of Neutrosophic sharpness. In other words, the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Neutrosophic SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Neutrosophic SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Neutrosophic SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-List-Coloring is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Neutrosophic SuperHyperClasses of the connected loopless Neutrosophic SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-List-Coloring. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Neutrosophic SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Neutrosophic structure of the Neutrosophic R-List-Coloring decorates the Neutrosophic SuperHyperVertices don&#39;t have received any Neutrosophic connections so as this Neutrosophic style implies different versions of Neutrosophic SuperHyperEdges with the maximum Neutrosophic cardinality in the terms of Neutrosophic SuperHyperVertices are spotlight. The lower Neutrosophic bound is to have the maximum Neutrosophic groups of Neutrosophic SuperHyperVertices have perfect Neutrosophic connections inside each of SuperHyperEdges and the outside of this Neutrosophic SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Neutrosophic SuperHyperGraph arising from its Neutrosophic properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Neutrosophic SuperHyperVertex in the targeted Neutrosophic SuperHyperSet, then there&#39;s no Neutrosophic connection. Furthermore, the Neutrosophic existence of one Neutrosophic SuperHyperVertex has no&nbsp; Neutrosophic effect to talk about the Neutrosophic R-List-Coloring. Since at least two Neutrosophic SuperHyperVertices involve to make a title in the Neutrosophic background of the Neutrosophic SuperHyperGraph. The Neutrosophic SuperHyperGraph is obvious if it has no Neutrosophic SuperHyperEdge but at least two Neutrosophic SuperHyperVertices make the Neutrosophic version of Neutrosophic SuperHyperEdge. Thus in the Neutrosophic setting of non-obvious Neutrosophic SuperHyperGraph, there are at least one Neutrosophic SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Neutrosophic adjective for the initial Neutrosophic SuperHyperGraph, induces there&#39;s no Neutrosophic&nbsp; appearance of the loop Neutrosophic version of the Neutrosophic SuperHyperEdge and this Neutrosophic SuperHyperGraph is said to be loopless. The Neutrosophic adjective ``loop&#39;&#39; on the basic Neutrosophic framework engages one Neutrosophic SuperHyperVertex but it never happens in this Neutrosophic setting. With these Neutrosophic bases, on a Neutrosophic SuperHyperGraph, there&#39;s at least one Neutrosophic SuperHyperEdge thus there&#39;s at least a Neutrosophic R-List-Coloring has the Neutrosophic cardinality of a Neutrosophic SuperHyperEdge. Thus, a Neutrosophic R-List-Coloring has the Neutrosophic cardinality at least a Neutrosophic SuperHyperEdge. Assume a Neutrosophic SuperHyperSet $V\setminus V\setminus \{z\}.$ This Neutrosophic SuperHyperSet isn&#39;t a Neutrosophic R-List-Coloring since either the Neutrosophic SuperHyperGraph is an obvious Neutrosophic SuperHyperModel thus it never happens since there&#39;s no Neutrosophic usage of this Neutrosophic framework and even more there&#39;s no Neutrosophic connection inside or the Neutrosophic SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Neutrosophic contradiction with the term ``Neutrosophic R-List-Coloring&#39;&#39; since the maximum Neutrosophic cardinality never happens for this Neutrosophic style of the Neutrosophic SuperHyperSet and beyond that there&#39;s no Neutrosophic connection inside as mentioned in first Neutrosophic case in the forms of drawback for this selected Neutrosophic SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Neutrosophic case implies having the Neutrosophic style of on-quasi-triangle Neutrosophic style on the every Neutrosophic elements of this Neutrosophic SuperHyperSet. Precisely, the Neutrosophic R-List-Coloring is the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that some Neutrosophic amount of the Neutrosophic SuperHyperVertices are on-quasi-triangle Neutrosophic style. The Neutrosophic cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Neutrosophic bound is up. Thus the minimum Neutrosophic cardinality of the maximum Neutrosophic cardinality ends up the Neutrosophic discussion. The first Neutrosophic term refers to the Neutrosophic setting of the Neutrosophic SuperHyperGraph but this key point is enough since there&#39;s a Neutrosophic SuperHyperClass of a Neutrosophic SuperHyperGraph has no on-quasi-triangle Neutrosophic style amid some amount of its Neutrosophic SuperHyperVertices. This Neutrosophic setting of the Neutrosophic SuperHyperModel proposes a Neutrosophic SuperHyperSet has only some amount&nbsp; Neutrosophic SuperHyperVertices from one Neutrosophic SuperHyperEdge such that there&#39;s no Neutrosophic amount of Neutrosophic SuperHyperEdges more than one involving these some amount of these Neutrosophic SuperHyperVertices. The Neutrosophic cardinality of this Neutrosophic SuperHyperSet is the maximum and the Neutrosophic case is occurred in the minimum Neutrosophic situation. To sum them up, the Neutrosophic SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Neutrosophic cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Neutrosophic SuperHyperVertices such that there&#39;s distinct-covers-order-amount Neutrosophic SuperHyperEdges for amount of Neutrosophic SuperHyperVertices taken from the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Neutrosophic&nbsp; R-List-Coloring for the Neutrosophic SuperHyperGraph as used Neutrosophic background in the Neutrosophic terms of worst Neutrosophic case and the common theme of the lower Neutrosophic bound occurred in the specific Neutrosophic SuperHyperClasses of the Neutrosophic SuperHyperGraphs which are Neutrosophic free-quasi-triangle. &nbsp; \\ Assume a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Neutrosophic number of the Neutrosophic SuperHyperVertices. Then every Neutrosophic SuperHyperVertex has at least no Neutrosophic SuperHyperEdge with others in common. Thus those Neutrosophic SuperHyperVertices have the eligibles to be contained in a Neutrosophic R-List-Coloring. Those Neutrosophic SuperHyperVertices are potentially included in a Neutrosophic&nbsp; style-R-List-Coloring. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Neutrosophic&nbsp; SuperHyperVertices of the Neutrosophic SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices and there&#39;s only and only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Neutrosophic SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Neutrosophic R-List-Coloring is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Neutrosophic R-List-Coloring but with slightly differences in the maximum Neutrosophic cardinality amid those Neutrosophic type-SuperHyperSets of the Neutrosophic SuperHyperVertices. Thus the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Neutrosophic cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Neutrosophic R-List-Coloring. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices belong to the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-List-Coloring}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-List-Coloring}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Neutrosophic quasi-R-List-Coloring where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Neutrosophic intended SuperHyperVertices but in a Neutrosophic List-Coloring, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-List-Coloring is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-List-Coloring is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic List-Coloring in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-List-Coloring. \\ The obvious SuperHyperGraph has no Neutrosophic SuperHyperEdges. But the non-obvious Neutrosophic SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Neutrosophic optimal SuperHyperObject. It specially delivers some remarks on the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that there&#39;s distinct amount of Neutrosophic SuperHyperEdges for distinct amount of Neutrosophic SuperHyperVertices up to all&nbsp; taken from that Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices but this Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices is either has the maximum Neutrosophic SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Neutrosophic SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Neutrosophic SuperHyperEdge containing at least all Neutrosophic SuperHyperVertices. Thus it forms a Neutrosophic quasi-R-List-Coloring where the Neutrosophic completion of the Neutrosophic incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Neutrosophic embedded R-List-Coloring. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Neutrosophic SuperHyperCardinality and they&#39;re Neutrosophic SuperHyperOptimal. The less than two distinct types of Neutrosophic SuperHyperVertices are included in the minimum Neutrosophic style of the embedded Neutrosophic R-List-Coloring. The interior types of the Neutrosophic SuperHyperVertices are deciders. Since the Neutrosophic number of SuperHyperNeighbors are only&nbsp; affected by the interior Neutrosophic SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Neutrosophic SuperHyperSet for any distinct types of Neutrosophic SuperHyperVertices pose the Neutrosophic R-List-Coloring. Thus Neutrosophic exterior SuperHyperVertices could be used only in one Neutrosophic SuperHyperEdge and in Neutrosophic SuperHyperRelation with the interior Neutrosophic SuperHyperVertices in that&nbsp; Neutrosophic SuperHyperEdge. In the embedded Neutrosophic List-Coloring, there&#39;s the usage of exterior Neutrosophic SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Neutrosophic SuperHyperVertex has no connection, inside. Thus, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Neutrosophic R-List-Coloring. The Neutrosophic R-List-Coloring with the exclusion of the exclusion of all&nbsp; Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge and with other terms, the Neutrosophic R-List-Coloring with the inclusion of all Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge, is a Neutrosophic quasi-R-List-Coloring. To sum them up, in a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-List-Coloring minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-List-Coloring, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Neutrosophic R-List-Coloring has two titles. a Neutrosophic quasi-R-List-Coloring and its corresponded quasi-maximum Neutrosophic R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Neutrosophic number, there&#39;s a Neutrosophic quasi-R-List-Coloring with that quasi-maximum Neutrosophic SuperHyperCardinality in the terms of the embedded Neutrosophic SuperHyperGraph. If there&#39;s an embedded Neutrosophic SuperHyperGraph, then the Neutrosophic quasi-SuperHyperNotions lead us to take the collection of all the Neutrosophic quasi-R-List-Colorings for all Neutrosophic numbers less than its Neutrosophic corresponded maximum number. The essence of the Neutrosophic List-Coloring ends up but this essence starts up in the terms of the Neutrosophic quasi-R-List-Coloring, again and more in the operations of collecting all the Neutrosophic quasi-R-List-Colorings acted on the all possible used formations of the Neutrosophic SuperHyperGraph to achieve one Neutrosophic number. This Neutrosophic number is\\ considered as the equivalence class for all corresponded quasi-R-List-Colorings. Let $z_{\text{Neutrosophic Number}},S_{\text{Neutrosophic SuperHyperSet}}$ and $G_{\text{Neutrosophic List-Coloring}}$ be a Neutrosophic number, a Neutrosophic SuperHyperSet and a Neutrosophic List-Coloring. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}=\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic List-Coloring}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Neutrosophic List-Coloring is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic List-Coloring}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Neutrosophic List-Coloring. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic List-Coloring}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Neutrosophic List-Coloring poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic List-Coloring}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic List-Coloring}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Neutrosophic SuperHyperVertices such that any amount of its Neutrosophic SuperHyperVertices are incident to a Neutrosophic&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Neutrosophic&nbsp; Quasi-List-Coloring&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Neutrosophic&nbsp; Quasi-List-Coloring&#39;&#39; since ``Neutrosophic Quasi-List-Coloring&#39;&#39; happens ``Neutrosophic List-Coloring&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and background but ``Neutrosophic SuperHyperNeighborhood&#39;&#39; may not happens ``Neutrosophic List-Coloring&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Neutrosophic SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Neutrosophic Quasi-List-Coloring&#39;&#39;, and&nbsp; ``Neutrosophic List-Coloring&#39;&#39; are up. \\ Thus, let $z_{\text{Neutrosophic Number}},N_{\text{Neutrosophic SuperHyperNeighborhood}}$ and $G_{\text{Neutrosophic List-Coloring}}$ be a Neutrosophic number, a Neutrosophic SuperHyperNeighborhood and a Neutrosophic List-Coloring and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic List-Coloring}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-List-Coloring if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperVertices is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-List-Coloring. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-List-Coloring. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Neutrosophic R-List-Coloring}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge amid some Neutrosophic SuperHyperVertices instead of all given by \underline{\textbf{Neutrosophic List-Coloring}} is related to the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic List-Coloring is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic List-Coloring is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex. But the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-List-Coloring \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-List-Coloring. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Neutrosophic R-List-Coloring $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic List-Coloring \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ List-Coloring}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic SuperHyperEdge for some amount Neutrosophic&nbsp; SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic List-Coloring. There isn&#39;t&nbsp; only less than two Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Neutrosophic R-List-Coloring, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic List-Coloring, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Neutrosophic SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; R-List-Coloring&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic R-List-Coloring}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Neutrosophic free-triangle embedded SuperHyperModel and a Neutrosophic on-triangle embedded SuperHyperModel but also it&#39;s a Neutrosophic stable embedded SuperHyperModel. But all only non-obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic&nbsp; R-List-Coloring amid those obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic List-Coloring, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Neutrosophic R-List-Coloring. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic&nbsp; R-List-Coloring is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-List-Coloring if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Neutrosophic SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Neutrosophic SuperHyperVertices $r.$ Consider all Neutrosophic numbers of those Neutrosophic SuperHyperVertices from that Neutrosophic SuperHyperEdge excluding excluding more than $r$ distinct Neutrosophic SuperHyperVertices, exclude to any given Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices. Consider there&#39;s a Neutrosophic&nbsp; R-List-Coloring with the least cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality. Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Neutrosophic SuperHyperSet $S$ of&nbsp; the Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have&nbsp; some Neutrosophic SuperHyperVertices uniquely but it isn&#39;t a Neutrosophic R-List-Coloring. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have some SuperHyperVertices uniquely. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Neutrosophic cardinality of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices but it isn&#39;t a Neutrosophic R-List-Coloring. Since it \textbf{\underline{doesn&#39;t do}} the Neutrosophic procedure such that such that there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Neutrosophic SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Neutrosophic SuperHyperGraph $ESHG:(V,E),$ a Neutrosophic SuperHyperVertex, titled its Neutrosophic SuperHyperNeighbor,&nbsp; to that Neutrosophic SuperHyperVertex in the Neutrosophic SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Neutrosophic procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Neutrosophic SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Neutrosophic SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Neutrosophic SuperHyperNeighborhood. Thus the obvious Neutrosophic R-List-Coloring,&nbsp; $V_{ESHE}$ is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-List-Coloring,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Neutrosophic SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Neutrosophic SuperHyperVertices does forms any kind of Neutrosophic pairs are titled&nbsp;&nbsp; \underline{Neutrosophic SuperHyperNeighbors} in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Neutrosophic SuperHyperCardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic SuperHyperVertices uniquely. Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Any Neutrosophic R-List-Coloring only contains all interior Neutrosophic SuperHyperVertices and all exterior Neutrosophic SuperHyperVertices from the unique Neutrosophic SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Neutrosophic SuperHyperNeighbors in and there&#39;s all&nbsp; Neutrosophic SuperHyperNeighborhoods in with no exception minus all&nbsp; Neutrosophic SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Neutrosophic SuperHyperNeighborhoods and Neutrosophic SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; List-Coloring, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic List-Coloring. &nbsp;The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic List-Coloring. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Neutrosophic List-Coloring}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic List-Coloring is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic List-Coloring is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices. But the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic List-Coloring \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic List-Coloring. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Neutrosophic List-Coloring $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic List-Coloring \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ List-Coloring}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There aren&#39;t&nbsp; only less than three Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Neutrosophic List-Coloring, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic List-Coloring, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Neutrosophic SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; List-Coloring&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic List-Coloring}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-List-Coloring SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-List-Coloring SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. Then there&#39;s no at least one SuperHyperList-Coloring. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperList-Coloring could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperList-Coloring taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperList-Coloring taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperList-Coloring. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperList-Coloring could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E^{*}_i\}_{i=1}^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic List-Coloring SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^{|E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-List-Coloring}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-List-Coloring SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperList-Coloring taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperList-Coloring. The latter is straightforward. Then there&#39;s at least one SuperHyperList-Coloring. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperList-Coloring could be applied. The unique embedded SuperHyperList-Coloring proposes some longest SuperHyperList-Coloring excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperList-Coloring. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperList-Coloring in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperList-Coloring,&nbsp; Neutrosophic SuperHyperList-Coloring, and the Neutrosophic SuperHyperList-Coloring, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperList-Coloring is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperList-Coloring. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperList-Coloring=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperList-Coloring of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperList-Coloring \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperList-Coloring.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperList-Coloring and SuperHyperList-Coloring coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperList-Coloring if and only if it&#39;s a SuperHyperList-Coloring. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperList-Coloring if and only if it&#39;s a longest SuperHyperList-Coloring. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperList-Coloring is its SuperHyperList-Coloring and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperList-Coloring is its SuperHyperList-Coloring and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperList-Coloring isn&#39;t well-defined if and only if its SuperHyperList-Coloring isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperList-Coloring is well-defined if and only if its SuperHyperList-Coloring is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperList-Coloring/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperList-Coloring; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperList-Coloring; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperList-Coloring/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperList-Coloring; &nbsp; \item[$(ii):$] the SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperList-Coloring; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperList-Coloring/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperList-Coloring, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperList-Coloring, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperList-Coloring set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperList-Coloring. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperList-Coloring. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperList-Coloring; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperList-Coloring for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is an s-SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperList-Coloring, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperList-Coloring, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperList-Coloring. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperList-Coloring. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperList-Coloring. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperList-Coloring, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring or the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperList-Coloring} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperList-Coloring. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperList-Coloring} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperList-Coloring. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperList-Coloring and the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperList-Coloring and the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperList-Coloring and the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperList-Coloring and the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperList-Coloring, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperList-Coloring. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperList-Coloring, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperList-Coloring and the Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperList-Coloring&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperList-Coloring}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperList-Coloring}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&ldquo;#188 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Cut As Hyper Click On Super Cliche&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26134.01603). @ResearchGate: https://www.researchgate.net/publication/369147477 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- &nbsp; \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Cut As Hyper Click On Super Cliche } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Cut). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Cut pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Cut if the following expression is called Neutrosophic e-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*}&nbsp; Neutrosophic re-SuperHyperClique-Cut if the following expression is called Neutrosophic e-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &nbsp; &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Cut&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Cut if the following expression is called Neutrosophic v-SuperHyperClique-Cut criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut. ((Neutrosophic) SuperHyperClique-Cut). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; a Neutrosophic SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; an Extreme SuperHyperClique-Cut SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; a Neutrosophic V-SuperHyperClique-Cut if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; an Extreme V-SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Cut &nbsp;and Neutrosophic SuperHyperClique-Cut. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Cut is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Cut is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Cut . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Cut &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Cut . It&#39;s redefined a Neutrosophic SuperHyperClique-Cut &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Cut . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Cut until the SuperHyperClique-Cut, then it&#39;s officially called a ``SuperHyperClique-Cut&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Cut . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Cut &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Cut . For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; and a ``Neutrosophic SuperHyperClique-Cut &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Cut &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Cut &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Cut&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Cut&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Cut &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Cut .] SuperHyperClique-Cut . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Cut if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Cut &nbsp;or the strongest SuperHyperClique-Cut &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Cut, called SuperHyperClique-Cut, and the strongest SuperHyperClique-Cut, called Neutrosophic SuperHyperClique-Cut, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Cut. There isn&#39;t any formation of any SuperHyperClique-Cut but literarily, it&#39;s the deformation of any SuperHyperClique-Cut. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Cut theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperClique-Cut, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Cut or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Cut. There isn&#39;t any formation of any SuperHyperClique-Cut but literarily, it&#39;s the deformation of any SuperHyperClique-Cut. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Cut&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Cut and Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut, are figured out in sections ``&nbsp; SuperHyperClique-Cut&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39;. In the sense of tackling on getting results and in Clique-Cut to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Cut&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Cut&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Cut of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Cut of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E_a,E_b\in E&#39;: \\&amp;&amp; &nbsp;E_a\sim E_b; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Cut} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Cut} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Cut criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V_a,V_b\in V&#39;: \\&amp;&amp; &nbsp;V_a\sim V_b; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Cut} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Cut; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Cut SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Cut, Neutrosophic re-SuperHyperClique-Cut, Neutrosophic v-SuperHyperClique-Cut, and Neutrosophic rv-SuperHyperClique-Cut and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Cut; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Cut).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Cut such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Cut} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Cut such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Cut. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Cut more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Cut, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Cut&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Cut. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Cut} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperClique-Cut But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Any k-function Clique-Cut like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function Clique-Cut like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $m$ and $n$ propose special Clique-Cut. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability Clique-Cut $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Cut $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $X_n$ be a Neutrosophic Variable in a probability Clique-Cut (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Cut. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_i\}_{i\neq3}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}}=3z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_i\}_{i=1}^3. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{E_1,E_4,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=z^3. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_1,V_2,V_3,N,F\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=(\text{Four Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{V_i\}_{i=1}^5. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz^2. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_i,V_{13}\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =3z^2. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{V_{13},V_i\}_{i=4}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{V_i,V_{22}\}_{i=11}^{20}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_i,V_{13}\}_{i=1}^7. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =3z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^5. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_2,E_3,E_4,E_7\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=3z^4. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}}= 2z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; =5z^2. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{i=8}^{17}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}}=11z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_i\}_{V_i\in E_2}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =2z^{7}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(\text{Ten Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{V_1,V_i\}_{V_i\in E_6}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =|E_6|z^2. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; =\{R,M_6,L_6,F,P,J,M,V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{10}. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Cut, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{M_6,L_6,F,V_3,V_2,H_6,O_6,E_6,C_6,Z_5,W_5,V_{10}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =z^{12}. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Cut if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Cut minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Cut, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Cut is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Cut in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Cut. \end{proposition} \begin{proposition} &nbsp;Assume a simple Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then the Neutrosophic number of&nbsp; type-result-R-Clique-Cut has, the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality, is the Neutrosophic cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Neutrosophic type-result-R-Clique-Cut with the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Neutrosophic type-result-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic type-result-Clique-Cut is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Cut since neither amount of Neutrosophic SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Neutrosophic number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices but the maximum Neutrosophic cardinality indicates that these Neutrosophic&nbsp; type-SuperHyperSets couldn&#39;t give us the Neutrosophic lower bound in the term of Neutrosophic sharpness. In other words, the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Neutrosophic SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Neutrosophic SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Neutrosophic SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Cut is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Neutrosophic SuperHyperClasses of the connected loopless Neutrosophic SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Cut. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Neutrosophic SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Neutrosophic structure of the Neutrosophic R-Clique-Cut decorates the Neutrosophic SuperHyperVertices don&#39;t have received any Neutrosophic connections so as this Neutrosophic style implies different versions of Neutrosophic SuperHyperEdges with the maximum Neutrosophic cardinality in the terms of Neutrosophic SuperHyperVertices are spotlight. The lower Neutrosophic bound is to have the maximum Neutrosophic groups of Neutrosophic SuperHyperVertices have perfect Neutrosophic connections inside each of SuperHyperEdges and the outside of this Neutrosophic SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Neutrosophic SuperHyperGraph arising from its Neutrosophic properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Neutrosophic SuperHyperVertex in the targeted Neutrosophic SuperHyperSet, then there&#39;s no Neutrosophic connection. Furthermore, the Neutrosophic existence of one Neutrosophic SuperHyperVertex has no&nbsp; Neutrosophic effect to talk about the Neutrosophic R-Clique-Cut. Since at least two Neutrosophic SuperHyperVertices involve to make a title in the Neutrosophic background of the Neutrosophic SuperHyperGraph. The Neutrosophic SuperHyperGraph is obvious if it has no Neutrosophic SuperHyperEdge but at least two Neutrosophic SuperHyperVertices make the Neutrosophic version of Neutrosophic SuperHyperEdge. Thus in the Neutrosophic setting of non-obvious Neutrosophic SuperHyperGraph, there are at least one Neutrosophic SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Neutrosophic adjective for the initial Neutrosophic SuperHyperGraph, induces there&#39;s no Neutrosophic&nbsp; appearance of the loop Neutrosophic version of the Neutrosophic SuperHyperEdge and this Neutrosophic SuperHyperGraph is said to be loopless. The Neutrosophic adjective ``loop&#39;&#39; on the basic Neutrosophic framework engages one Neutrosophic SuperHyperVertex but it never happens in this Neutrosophic setting. With these Neutrosophic bases, on a Neutrosophic SuperHyperGraph, there&#39;s at least one Neutrosophic SuperHyperEdge thus there&#39;s at least a Neutrosophic R-Clique-Cut has the Neutrosophic cardinality of a Neutrosophic SuperHyperEdge. Thus, a Neutrosophic R-Clique-Cut has the Neutrosophic cardinality at least a Neutrosophic SuperHyperEdge. Assume a Neutrosophic SuperHyperSet $V\setminus V\setminus \{z\}.$ This Neutrosophic SuperHyperSet isn&#39;t a Neutrosophic R-Clique-Cut since either the Neutrosophic SuperHyperGraph is an obvious Neutrosophic SuperHyperModel thus it never happens since there&#39;s no Neutrosophic usage of this Neutrosophic framework and even more there&#39;s no Neutrosophic connection inside or the Neutrosophic SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Neutrosophic contradiction with the term ``Neutrosophic R-Clique-Cut&#39;&#39; since the maximum Neutrosophic cardinality never happens for this Neutrosophic style of the Neutrosophic SuperHyperSet and beyond that there&#39;s no Neutrosophic connection inside as mentioned in first Neutrosophic case in the forms of drawback for this selected Neutrosophic SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Neutrosophic case implies having the Neutrosophic style of on-quasi-triangle Neutrosophic style on the every Neutrosophic elements of this Neutrosophic SuperHyperSet. Precisely, the Neutrosophic R-Clique-Cut is the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that some Neutrosophic amount of the Neutrosophic SuperHyperVertices are on-quasi-triangle Neutrosophic style. The Neutrosophic cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Neutrosophic bound is up. Thus the minimum Neutrosophic cardinality of the maximum Neutrosophic cardinality ends up the Neutrosophic discussion. The first Neutrosophic term refers to the Neutrosophic setting of the Neutrosophic SuperHyperGraph but this key point is enough since there&#39;s a Neutrosophic SuperHyperClass of a Neutrosophic SuperHyperGraph has no on-quasi-triangle Neutrosophic style amid some amount of its Neutrosophic SuperHyperVertices. This Neutrosophic setting of the Neutrosophic SuperHyperModel proposes a Neutrosophic SuperHyperSet has only some amount&nbsp; Neutrosophic SuperHyperVertices from one Neutrosophic SuperHyperEdge such that there&#39;s no Neutrosophic amount of Neutrosophic SuperHyperEdges more than one involving these some amount of these Neutrosophic SuperHyperVertices. The Neutrosophic cardinality of this Neutrosophic SuperHyperSet is the maximum and the Neutrosophic case is occurred in the minimum Neutrosophic situation. To sum them up, the Neutrosophic SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Neutrosophic cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Neutrosophic SuperHyperVertices such that there&#39;s distinct-covers-order-amount Neutrosophic SuperHyperEdges for amount of Neutrosophic SuperHyperVertices taken from the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Neutrosophic&nbsp; R-Clique-Cut for the Neutrosophic SuperHyperGraph as used Neutrosophic background in the Neutrosophic terms of worst Neutrosophic case and the common theme of the lower Neutrosophic bound occurred in the specific Neutrosophic SuperHyperClasses of the Neutrosophic SuperHyperGraphs which are Neutrosophic free-quasi-triangle. &nbsp; \\ Assume a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Neutrosophic number of the Neutrosophic SuperHyperVertices. Then every Neutrosophic SuperHyperVertex has at least no Neutrosophic SuperHyperEdge with others in common. Thus those Neutrosophic SuperHyperVertices have the eligibles to be contained in a Neutrosophic R-Clique-Cut. Those Neutrosophic SuperHyperVertices are potentially included in a Neutrosophic&nbsp; style-R-Clique-Cut. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Neutrosophic&nbsp; SuperHyperVertices of the Neutrosophic SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices and there&#39;s only and only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Neutrosophic SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Neutrosophic R-Clique-Cut is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Neutrosophic R-Clique-Cut but with slightly differences in the maximum Neutrosophic cardinality amid those Neutrosophic type-SuperHyperSets of the Neutrosophic SuperHyperVertices. Thus the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Neutrosophic cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Neutrosophic R-Clique-Cut. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices belong to the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Cut}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Cut}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Neutrosophic quasi-R-Clique-Cut where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Neutrosophic intended SuperHyperVertices but in a Neutrosophic Clique-Cut, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Cut is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Cut is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Cut in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Cut. \\ The obvious SuperHyperGraph has no Neutrosophic SuperHyperEdges. But the non-obvious Neutrosophic SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Neutrosophic optimal SuperHyperObject. It specially delivers some remarks on the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that there&#39;s distinct amount of Neutrosophic SuperHyperEdges for distinct amount of Neutrosophic SuperHyperVertices up to all&nbsp; taken from that Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices but this Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices is either has the maximum Neutrosophic SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Neutrosophic SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Neutrosophic SuperHyperEdge containing at least all Neutrosophic SuperHyperVertices. Thus it forms a Neutrosophic quasi-R-Clique-Cut where the Neutrosophic completion of the Neutrosophic incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Neutrosophic embedded R-Clique-Cut. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Neutrosophic SuperHyperCardinality and they&#39;re Neutrosophic SuperHyperOptimal. The less than two distinct types of Neutrosophic SuperHyperVertices are included in the minimum Neutrosophic style of the embedded Neutrosophic R-Clique-Cut. The interior types of the Neutrosophic SuperHyperVertices are deciders. Since the Neutrosophic number of SuperHyperNeighbors are only&nbsp; affected by the interior Neutrosophic SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Neutrosophic SuperHyperSet for any distinct types of Neutrosophic SuperHyperVertices pose the Neutrosophic R-Clique-Cut. Thus Neutrosophic exterior SuperHyperVertices could be used only in one Neutrosophic SuperHyperEdge and in Neutrosophic SuperHyperRelation with the interior Neutrosophic SuperHyperVertices in that&nbsp; Neutrosophic SuperHyperEdge. In the embedded Neutrosophic Clique-Cut, there&#39;s the usage of exterior Neutrosophic SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Neutrosophic SuperHyperVertex has no connection, inside. Thus, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Neutrosophic R-Clique-Cut. The Neutrosophic R-Clique-Cut with the exclusion of the exclusion of all&nbsp; Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge and with other terms, the Neutrosophic R-Clique-Cut with the inclusion of all Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge, is a Neutrosophic quasi-R-Clique-Cut. To sum them up, in a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Cut minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Cut, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Neutrosophic R-Clique-Cut has two titles. a Neutrosophic quasi-R-Clique-Cut and its corresponded quasi-maximum Neutrosophic R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Neutrosophic number, there&#39;s a Neutrosophic quasi-R-Clique-Cut with that quasi-maximum Neutrosophic SuperHyperCardinality in the terms of the embedded Neutrosophic SuperHyperGraph. If there&#39;s an embedded Neutrosophic SuperHyperGraph, then the Neutrosophic quasi-SuperHyperNotions lead us to take the collection of all the Neutrosophic quasi-R-Clique-Cuts for all Neutrosophic numbers less than its Neutrosophic corresponded maximum number. The essence of the Neutrosophic Clique-Cut ends up but this essence starts up in the terms of the Neutrosophic quasi-R-Clique-Cut, again and more in the operations of collecting all the Neutrosophic quasi-R-Clique-Cuts acted on the all possible used formations of the Neutrosophic SuperHyperGraph to achieve one Neutrosophic number. This Neutrosophic number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Cuts. Let $z_{\text{Neutrosophic Number}},S_{\text{Neutrosophic SuperHyperSet}}$ and $G_{\text{Neutrosophic Clique-Cut}}$ be a Neutrosophic number, a Neutrosophic SuperHyperSet and a Neutrosophic Clique-Cut. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}=\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Cut}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Neutrosophic Clique-Cut is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Cut}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Neutrosophic Clique-Cut. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Cut}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Neutrosophic Clique-Cut poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Cut}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Cut}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Neutrosophic SuperHyperVertices such that any amount of its Neutrosophic SuperHyperVertices are incident to a Neutrosophic&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Neutrosophic&nbsp; Quasi-Clique-Cut&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Neutrosophic&nbsp; Quasi-Clique-Cut&#39;&#39; since ``Neutrosophic Quasi-Clique-Cut&#39;&#39; happens ``Neutrosophic Clique-Cut&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and background but ``Neutrosophic SuperHyperNeighborhood&#39;&#39; may not happens ``Neutrosophic Clique-Cut&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Neutrosophic SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Neutrosophic Quasi-Clique-Cut&#39;&#39;, and&nbsp; ``Neutrosophic Clique-Cut&#39;&#39; are up. \\ Thus, let $z_{\text{Neutrosophic Number}},N_{\text{Neutrosophic SuperHyperNeighborhood}}$ and $G_{\text{Neutrosophic Clique-Cut}}$ be a Neutrosophic number, a Neutrosophic SuperHyperNeighborhood and a Neutrosophic Clique-Cut and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Cut}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Cut if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperVertices is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Cut. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Cut. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Neutrosophic R-Clique-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge amid some Neutrosophic SuperHyperVertices instead of all given by \underline{\textbf{Neutrosophic Clique-Cut}} is related to the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Cut is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Cut is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex. But the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Cut \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Cut. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Neutrosophic R-Clique-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic SuperHyperEdge for some amount Neutrosophic&nbsp; SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Cut. There isn&#39;t&nbsp; only less than two Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Neutrosophic R-Clique-Cut, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Cut, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Neutrosophic SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; R-Clique-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic R-Clique-Cut}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Neutrosophic free-triangle embedded SuperHyperModel and a Neutrosophic on-triangle embedded SuperHyperModel but also it&#39;s a Neutrosophic stable embedded SuperHyperModel. But all only non-obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic&nbsp; R-Clique-Cut amid those obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic Clique-Cut, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Neutrosophic R-Clique-Cut. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic&nbsp; R-Clique-Cut is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Cut if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Neutrosophic SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Neutrosophic SuperHyperVertices $r.$ Consider all Neutrosophic numbers of those Neutrosophic SuperHyperVertices from that Neutrosophic SuperHyperEdge excluding excluding more than $r$ distinct Neutrosophic SuperHyperVertices, exclude to any given Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices. Consider there&#39;s a Neutrosophic&nbsp; R-Clique-Cut with the least cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality. Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Neutrosophic SuperHyperSet $S$ of&nbsp; the Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have&nbsp; some Neutrosophic SuperHyperVertices uniquely but it isn&#39;t a Neutrosophic R-Clique-Cut. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have some SuperHyperVertices uniquely. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Neutrosophic cardinality of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices but it isn&#39;t a Neutrosophic R-Clique-Cut. Since it \textbf{\underline{doesn&#39;t do}} the Neutrosophic procedure such that such that there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Neutrosophic SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Neutrosophic SuperHyperGraph $ESHG:(V,E),$ a Neutrosophic SuperHyperVertex, titled its Neutrosophic SuperHyperNeighbor,&nbsp; to that Neutrosophic SuperHyperVertex in the Neutrosophic SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Neutrosophic procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Neutrosophic SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Neutrosophic SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Neutrosophic SuperHyperNeighborhood. Thus the obvious Neutrosophic R-Clique-Cut,&nbsp; $V_{ESHE}$ is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Cut,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Neutrosophic SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Neutrosophic SuperHyperVertices does forms any kind of Neutrosophic pairs are titled&nbsp;&nbsp; \underline{Neutrosophic SuperHyperNeighbors} in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Neutrosophic SuperHyperCardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic SuperHyperVertices uniquely. Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Any Neutrosophic R-Clique-Cut only contains all interior Neutrosophic SuperHyperVertices and all exterior Neutrosophic SuperHyperVertices from the unique Neutrosophic SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Neutrosophic SuperHyperNeighbors in and there&#39;s all&nbsp; Neutrosophic SuperHyperNeighborhoods in with no exception minus all&nbsp; Neutrosophic SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Neutrosophic SuperHyperNeighborhoods and Neutrosophic SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Cut, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Cut. &nbsp;The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Cut. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Neutrosophic Clique-Cut}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Cut is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Cut is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices. But the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Cut \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Cut. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Neutrosophic Clique-Cut $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Cut \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Cut}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There aren&#39;t&nbsp; only less than three Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Neutrosophic Clique-Cut, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Cut, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Neutrosophic SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; Clique-Cut&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic Clique-Cut}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Cut SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Cut SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|E_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^2. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}| \text{Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E_i\in\{E_a~|~ |E_a|=\max |E_b|_{E_b\in E_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Cut could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Cut taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E_i\}_{i=1}^{|P_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^{|P_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Cut taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Cut. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Cut could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{E^{*}_1,E^{*}_2,E^{*}_3\}_{E^{*}_i\in E^{*}_{NSHG}|}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Cut SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E^{*}_{NSHG}| \text{Choose Three})z^3. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Cut}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Cut SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Cut taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Cut. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Cut. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Cut could be applied. The unique embedded SuperHyperClique-Cut proposes some longest SuperHyperClique-Cut excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperClique-Cut. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Cut in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Cut,&nbsp; Neutrosophic SuperHyperClique-Cut, and the Neutrosophic SuperHyperClique-Cut, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperClique-Cut is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperClique-Cut. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperClique-Cut=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Cut of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Cut \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperClique-Cut.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperClique-Cut and SuperHyperClique-Cut coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperClique-Cut if and only if it&#39;s a SuperHyperClique-Cut. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Cut if and only if it&#39;s a longest SuperHyperClique-Cut. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Cut is its SuperHyperClique-Cut and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Cut is its SuperHyperClique-Cut and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Cut isn&#39;t well-defined if and only if its SuperHyperClique-Cut isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Cut is well-defined if and only if its SuperHyperClique-Cut is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Cut/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Cut; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Cut/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Cut; &nbsp; \item[$(ii):$] the SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Cut; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperClique-Cut/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Cut, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Cut, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Cut set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Cut. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Cut; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Cut for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Cut, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Cut, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Cut. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Cut. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Cut, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Cut} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperClique-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Cut} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperClique-Cut. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Cut and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Cut and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Cut and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Cut and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Cut, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Cut. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Cut, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Cut and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Cut&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Cut}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperClique-Cut}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}

&#x0D; &#x0D; &#x0D; The following petition was circulated in Dubbo in May 2003:&#x0D; &#x0D; Mr Carr,&#x0D; We the undersigned are concerned citizens, tired of Government inaction in dealing with young children who are causing distress around our cities. Children 8, 9 &amp; 10 year olds are roaming the streets day &amp; night and Harassment of the elderly &amp; Intimidation, Truancy, Enter &amp; Steal, Vandalism and Shoplifting are causing major concern in our area. Young children, too young to deal with now, grow up bigger &amp; stronger as they move into the adult world of crime. At present they seem to be untouchable with many people with good intentions making excuses. We need laws in place to help them toward a better future and a safer environment for us all.&#x0D; You have achieved much in relation to crime &amp; punishment with Goals &amp; we need to save this coming generation from a life of crime.&#x0D; Parents should be made responsible for their children’s actions.&#x0D; If parents can’t or won’t, the children should be placed in suitable accommodation where Self Esteem, Education, Health &amp; Responsibilities are taught.&#x0D; Mr Carr, NSW has an opportunity to lead the country in what is a national problem.&#x0D; &#x0D; &#x0D; Anyone shopping in Dubbo’s main street in at that time would have found copies of this petition presented in neat stacks on sales counters and reception desks in the majority of retail stores and other small businesses. One month later, 11 000 people from a population of 36 000 had signed the petition. In examining why such a severe proposal arose, and why it garnered so much support, I am positioning the events in the lead up to and following the petition as part of continuing processes of domination and exclusion within race relations. The theoretical framework for this relies on Roxanne Lynn Doty’s notion of ‘statecraft’, which she draws from the work of Deleuze and Guattari.&#x0D; &#x0D; The main street in Dubbo is a place for consumption and public display. People are welcome as long as they observe the rules ‘concerned citizens’ deem appropriate for that space. The main street is the image of the town, invested with symbolic capital. Those who threaten the construction of a particular image are literally out of place. &#x0D; &#x0D; The petition is a matter of ‘race relations’, or more accurately, domination and resistance, despite no specific indications in the document’s wording. In official and pseudo-official situations in Dubbo, in local newspapers and radio, ‘uncontrollable’ had become a substitute for Aboriginal. Warren Mundine, at the time Deputy Mayor and Dubbo’s only Indigenous Councillor, said, ‘people might say “we haven’t mentioned Aboriginal kids” but everyone knows what they are talking about’ (O’Malley 3). To understand why there were calls for widespread and systematic forcible removal of Aboriginal children – a proposed measure that resonated with the darkest periods of pre-1970s style of removal – we need to contextualise it with discussion of key events in the lead up to the petition’s appearance.&#x0D; &#x0D; A local radio announcer, Leo de Kroo, whose morning talk-back show emulated the programs of metropolitan ‘shock-jocks’ instigated the petition after some months of on-air attacks on young people in Dubbo. Like some metropolitan stations, 2DU aligned itself with conservative political parties. On his show, de Kroo directly and indirectly supported Coalition policies and initiatives such as lobbying for the Parental Responsibility Act to operate in Dubbo as it does in Orange, and to lower the age at which children could be charged with crimes. De Kroo’s individual motivations is partially explained by his political opportunism, but the wider processes his actions are a part of, and the large degree of support for petition from people in Dubbo, are more interesting. &#x0D; &#x0D; De Kroo’s claim that Dubbo was a town ‘out of control’ and in a ‘bad spot with youth on the streets’ (Roberts, “Voice of Youth” 2) came at a time when crime rates were falling. In February 2003 Local Area Commander Supt Ian Lovell said that crime had dropped to ‘unheard of [levels]. Dubbo hasn’t experienced such low levels of crime in years’ (Jacobson, “Viking Cuts” 11). In March the Orana Crime Management Unit declared assaults, car accidents, malicious damage, stealing and traffic offences were down from the previous month (Jacobson, “Burglaries Falling” 4). Again in May Supt Lovell declared a similar range of crimes were down from the previous month (Jacobson, “Crime Cools” 4). Typically, stories about crime statistics were published in the middle sections of the local paper, while complaints about crime were almost invariably on the front page, but this was still a time when one might expect the community to be feeling safer in their everyday lives. However, despite consecutive months of falling crime rates, some inhabitants clearly felt insecure. This is evidenced by the support for the petition one month later, and interviews by the local newspaper, such as one with main street retailers who said they believed crime was spiralling out of control, that children were ‘terrorising staff’, that it was no longer safe to go to work, and that it was a matter of time before a shop assistant would be ‘stuck’ with a drug user’s needle (Jacobson, “We’re Sick of It” 1). To examine this situation I am turning to Doty’s concept of ‘statecraft’, desire and exclusion, which she bases on the work of Deleuze and Guattari.&#x0D; &#x0D; Doty draws on Deleuze and Guattari’s concept of desire to suggest ‘the state’ is always an unattainable desire for order. Desire for Deleuze and Guattari is ‘not a lack or fantasy or pleasure’ (Doty 1) but instead is a free flowing energy, a creative flow of production, that is coded and channelled by forces within the social body (Deleuze and Guattari). Social practices that channel and code desire create systems of meanings, values, hierarchies, inclusions and exclusions (Doty). So desire possesses the simultaneous potential for liberating, breaking down and deterritorialising, as well as for repression, segmentation and reterritorialisation. Deleuze and Guattari see this tension as existing in two poles of desire: ‘the schizophrenic pole deterritorialises and threatens to destroy the codes that inscribe meaning to social forms. The paranoiac pole presses for order and contains an inherent tendency toward despotism, repression, fascism’ (Doty 10).&#x0D; &#x0D; These poles, in Deleuze and Guattari’s writing, are tied to economic systems. Doty, paraphrasing Karl Polaryi – a philosopher whose work critiques liberal economic systems – says that ‘the self-adjusting market of capitalism could not exist for any length of time without annihilating society’ (qtd. in Doty 7). The destabilising flows of liberal economies are always countered by some form of governmentality which reinforces society through welfare, regulation and other protections and interventions. Capitalism ‘liberates flows of desire, but under the social conditions that define its limits and its own dissolution’ (Deleuze and Guattari 139). Capitalism belongs to the fluid pole of desire, the schizophrenic pole, and the fixing, regulating forces of ‘the state’ belong to the paranoiac pole. The state, then, is a desire for order, a movement towards fixedness, rigidness. Doty calls the set of practices that enable these movements ‘statecraft’.&#x0D; &#x0D; It is Doty’s conception of ‘the state’ and statecraft that I have tried to apply to the events that took place in Dubbo. ‘We can speak of “the state” only in a very provisional sense. It is not unitary. It is not an actor. It is not even a concrete “thing”… There is no such thing as “the state”, only a powerful desire that pervades the social realm’ (Doty 12). For Doty, the state is nothing but practices of statecraft that can originate in government bureaucracies, churches, corporations, theatres, newspapers, in our backyards, in our living rooms and bedrooms. They can come from the Federal or State Government, the local Council, the editor of the local newspaper, a journalist, a documentary maker, teenagers exchanging SMSes, the gossip mongers in the street and couples drinking tea in their kitchens.&#x0D; &#x0D; There were a number of key events in the lead up to the release of the petition in Dubbo that exacerbated the paranoiac pole of desire, the desire for order. At the start of 2003 the Federal Government was running an anti-terrorism campaign through television ads and later through a kit delivered to households across Australia. This was to generate fear to try to garner support for its involvement in the invasion of Iraq in March 2003. Also, election campaigns for the March State elections were run on Law and Order platforms. The NSW Government organised an Operation Viking which took place in Dubbo and was the largest police operation ever undertaken outside of Sydney (Jacobson, “Viking Cuts” 11). Hundreds of police officers were bussed in from Sydney and other cities and the ‘high visibility’ policing action included the use of a helicopter which shone a spotlight into people’s backyards. One local Councillor said the operation gave the impression there was ‘some national emergency’ (Jacobson, “Police” 1). Indicative of the tendency for these actions generate more fear are the comments of Supt Lovell, ‘I feel upset when people have to be briefed and calmed down after an operation that was designed to do just that’ (Roberts, “Operation” 1). Then in April there was an arson attack on Dubbo’s Council buildings. The offices were razed and this event is significant because the high public profile and uncommon nature of the incident, and because the accused perpetrators were the same ‘uncontrollable’ children said to be roaming the streets. &#x0D; &#x0D; These events contributed to an elevated sense of fear an anxiety around the same time the petition was circulated despite the fact that crime figures were falling. Indeed, the bulk of the complaints against ‘uncontrollable children’ were not that they were committing any particular crimes. The main street retailers quoted earlier felt intimidated by their presence. The complaints were of ‘antisocial behaviour’ and of minor annoyances incommensurable to the drastic and violent measures called for to deal with perceived problems. Their alleged swearing, spitting and talking in groups – in essence, their mere presence on the street – made people feel unsafe. &#x0D; &#x0D; This is due to a facet of statecraft – the exclusion of certain groups who are deemed antithetical to the social order. Doty notes the poor are often those rendered a threat to social order because of their lack of fixedness, their perceived lack of morals, the public display of behaviour the inside group consider private, and the different priorities relative to the inside group. Any threats to the social order are dealt with violently, as practices of statecraft inherently tend towards violence (Doty). In this case, the call for Government to forcibly remove children is violent, but it can also manifest in vigilante action, over zealous arrests, or casual assaults on the streets of Dubbo. Aboriginal people become an ‘excluded other that is itself constituted by the social order from which it is excluded’ (Doty 14). Practices of statecraft create excluded groups (Indigenous people’s claim to land is certainly antithetical to the social order of colonisers) and these outside groups in turn become feared by the inside group. &#x0D; &#x0D; The petition was never submitted to the Premier, nor tabled in parliament in its own right. Instead it was simply used by NSW National Party leader Andrew Stoner to strengthen his arguments for lowering the age at which children could be charged for crimes. The fact that it was not submitted to the Premier suggests the aim of the petition was to create a sense that all Aboriginal adults are criminals, and that Aboriginal culture is an inherently criminal one. ‘Young children, too young to deal with now, grow up bigger &amp; stronger as they move into the adult world of crime’ (Petition). A local Aboriginal leader, after convening a meeting in response to the petition, said, ‘thinly-veiled comments made on radio and circulating within the community made it clear a lot of Dubbo residents believed Aboriginal people were to blame for all the city’s ills’ (Hodder, “Meeting” 2).&#x0D; &#x0D; The purpose of the petition is to justify exclusion of anyone deemed a threat to the stability of the social order. The Carr government dismissed calls for children to be removed from their parents, but responded to the petition by declaring there would be more Operation Vikings for Dubbo (Stone 1). The desire for order, an order always unattainable, intensified by generation of fear, has enabled vigilante action on the streets of Dubbo. The action targets those the petition constructed as ‘uncontrollable’. Retailers in the CBD have set up networks amongst themselves, with the help of cameras, mobile phones and sirens to assail anyone they suspect of being threatening, or of shoplifting or making a mess of their stores (Hodder, “Retailers” 10). Recently ‘I [heart] Dubbo’ T-shirts were manufactured in a campaign to counter the negative media coverage generated by the petition and subsequent racial tensions. It was a defiant display of localism that seemed specifically designed to shun criticisms of Dubbo-style race relations and separate those who say they want success for the town from those who are said to want to destroy it. After identifying practices of statecraft in this series of events, what is needed is an examination of methods and practices for evading or deterritorialising movements towards order. &#x0D; &#x0D; References&#x0D; &#x0D; Deleuze, Gilles, and Félix Guattari. Anti-Oedipus : Capitalism and Schizophrenia. Minneapolis: University of Minnesota Press, 1983. Doty, Roxanne Lynn. Anti-Immigrantism in Western Democracies : Statecraft, Desire and the Politics of Exclusion. New York, N.Y.: Routledge, 2003. Hodder, S. “Meeting Declared a Success.” Daily Liberal 12 June 2003: 2. ———. “Retailers Call on Each Other to Fight Thieves.” Daily Liberal 10 November 2004: 2. Jacobson, B. “Viking Cuts City Crime: Police Chief.” Daily Liberal 6 February 2003: 11. ———. “Burglaries Falling.” Daily Liberal 5 March 2003: 4. ———. “Crime Cools Down.” Daily Liberal 6 May 2003: 4. ———. “Police ‘Picked on’ Youth in Blitz.” Daily Liberal 5 February 2003: 1. ———. “We’re Sick of It.” Daily Liberal 3 April 2003: 1. O’Malley, N. “Brogden Backs Dubbo Radio Host’s Hard Line on Child Crime.” Sydney Morning Herald 19 June 2003: 3. Roberts, N. “Operation ‘Was Not Perfect’.” Daily Liberal 7 February 2003: 1. ———. “Voice of Youth to Be Heard across Radio Airwaves.” Daily Liberal 9 May 2003: 2. Stone, K. “Carr Takes Control.” Daily Liberal 18 June 2003: 1.&#x0D; &#x0D; &#x0D; &#x0D; &#x0D; Citation reference for this article&#x0D; &#x0D; MLA Style&#x0D; Muir, Cameron. "Vigilant Citizens: Statecraft and Exclusion in Dubbo City." M/C Journal 9.3 (2006). echo date('d M. Y'); ?&gt; &lt;http://journal.media-culture.org.au/0607/02-muir.php&gt;. APA Style&#x0D; Muir, C. (Jul. 2006) "Vigilant Citizens: Statecraft and Exclusion in Dubbo City," M/C Journal, 9(3). Retrieved echo date('d M. Y'); ?&gt; from &lt;http://journal.media-culture.org.au/0607/02-muir.php&gt;. &#x0D;

&ldquo;#191 Article&rdquo; Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Decompositions As Hyper Decompile On Super Decommission&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18780.87683). @ResearchGate: https://www.researchgate.net/publication/369187021 @Scribd: https://www.scribd.com/document/- @ZENODO_ORG: https://zenodo.org/record/- @academia: https://www.academia.edu/- &nbsp; -- \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} \usepackage{fancyhdr} \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } \fancyfoot[LE,RO]{Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA } % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Clique-Decompositions As Hyper Decompile On Super Decommission } } \newline \newline Henry Garrett &middot; Independent Researcher &middot; Department of Mathematics &middot; DrHenryGarrett@gmail.com &middot; Manhattan, NY, USA % authors go here: \end{flushleft} \section{ABSTRACT} In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperClique-Decompositions). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a Clique-Decompositions pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called Neutrosophic e-SuperHyperClique-Decompositions if the following expression is called Neutrosophic e-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp;Neutrosophic re-SuperHyperClique-Decompositions if the following expression is called Neutrosophic e-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp;and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperClique-Decompositions&nbsp; if the following expression is called Neutrosophic v-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} &nbsp; Neutrosophic rv-SuperHyperClique-Decompositions if the following expression is called Neutrosophic v-SuperHyperClique-Decompositions criteria holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions. ((Neutrosophic) SuperHyperClique-Decompositions). &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called an Extreme SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; a Neutrosophic SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; an Extreme SuperHyperClique-Decompositions SuperHyperPolynomial&nbsp; if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; a Neutrosophic V-SuperHyperClique-Decompositions if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; an Extreme V-SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.&nbsp; In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperClique-Decompositions &nbsp;and Neutrosophic SuperHyperClique-Decompositions. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and &nbsp;SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer&#39;s Recognition&#39;&#39; are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex&#39;&#39; but the relations amid them all officially called ``SuperHyperEdge&#39;&#39;. The frameworks ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39; are chosen and elected to research about ``Cancer&#39;s Recognition&#39;&#39;. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer&#39;s Recognition&#39;&#39;. Some avenues are posed to pursue this research. It&#39;s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then $\delta-$SuperHyperClique-Decompositions is a maximal &nbsp; &nbsp;of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of &nbsp;SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a Neutrosophic $\delta-$SuperHyperClique-Decompositions is a maximal Neutrosophic &nbsp; &nbsp; of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of &nbsp;SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta;$ and $ |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta.$ The first Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta-$SuperHyperDefensive &nbsp; It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a SuperHyperClique-Decompositions . Since there&#39;s more ways to get type-results to make a SuperHyperClique-Decompositions &nbsp;more understandable. For the sake of having Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``SuperHyperClique-Decompositions &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a SuperHyperClique-Decompositions . It&#39;s redefined a Neutrosophic SuperHyperClique-Decompositions &nbsp;if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph&#39;&#39; with the key points, &nbsp; ``The Values of The Vertices \&amp; The Number of Position in Alphabet&#39;&#39;, ``The Values of The SuperVertices\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The Edges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The HyperEdges\&amp;The maximum Values of Its Vertices&#39;&#39;, ``The Values of The SuperHyperEdges\&amp;The maximum Values of Its Endpoints&#39;&#39;. To get structural examples and instances, I&#39;m going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyperClique-Decompositions . It&#39;s the main. It&#39;ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there&#39;s a need to have all SuperHyperClique-Decompositions until the SuperHyperClique-Decompositions, then it&#39;s officially called a ``SuperHyperClique-Decompositions&#39;&#39; but otherwise, it isn&#39;t a SuperHyperClique-Decompositions . There are some instances about the clarifications for the main definition titled a ``SuperHyperClique-Decompositions &#39;&#39;. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperClique-Decompositions . For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``redefine&#39;&#39; the notion of a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; and a ``Neutrosophic SuperHyperClique-Decompositions &#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. Assume a Neutrosophic SuperHyperGraph. It&#39;s redefined ``Neutrosophic SuperHyperGraph&#39;&#39; if the intended Table holds. And a SuperHyperClique-Decompositions &nbsp;are redefined to a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; if the intended Table holds. It&#39;s useful to define ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyperClique-Decompositions &nbsp;more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus &nbsp;SuperHyperPath, &nbsp;SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and &nbsp; SuperHyperWheel, are ``Neutrosophic SuperHyperPath&#39;&#39;, ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39;, ``Neutrosophic SuperHyperStar&#39;&#39;, ``Neutrosophic SuperHyperBipartite&#39;&#39;, ``Neutrosophic SuperHyperMultiPartite&#39;&#39;, and ``Neutrosophic SuperHyperWheel&#39;&#39; if the intended Table holds. &nbsp;A SuperHyperGraph has a ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39; where it&#39;s the strongest [the maximum Neutrosophic value from all the SuperHyperClique-Decompositions &nbsp;amid the maximum value amid all SuperHyperVertices from a SuperHyperClique-Decompositions .] SuperHyperClique-Decompositions . A graph is a SuperHyperUniform if it&#39;s a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It&#39;s SuperHyperPath if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it&#39;s SuperHyperClique-Decompositions if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; it&#39;s SuperHyperStar it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; it&#39;s SuperHyperBipartite it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it&#39;s SuperHyperMultiPartite &nbsp;it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it&#39;s a SuperHyperWheel if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. In this SuperHyperModel, The ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperVertices&#39;&#39; and the common and intended properties between ``specific&#39;&#39; cells and ``specific group&#39;&#39; of cells are SuperHyperModeled as ``SuperHyperEdges&#39;&#39;. Sometimes, it&#39;s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic&#39;&#39;. In the future research, the foundation will be based on the ``Cancer&#39;s Recognition&#39;&#39; and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, &nbsp;SuperHyperWheel). The aim is to find either the longest SuperHyperClique-Decompositions &nbsp;or the strongest SuperHyperClique-Decompositions &nbsp;in those Neutrosophic SuperHyperModels. For the longest SuperHyperClique-Decompositions, called SuperHyperClique-Decompositions, and the strongest SuperHyperClique-Decompositions, called Neutrosophic SuperHyperClique-Decompositions, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Decompositions. There isn&#39;t any formation of any SuperHyperClique-Decompositions but literarily, it&#39;s the deformation of any SuperHyperClique-Decompositions. It, literarily, deforms and it doesn&#39;t form. &nbsp;A basic familiarity with Neutrosophic &nbsp;SuperHyperClique-Decompositions theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed. \\ \vspace{4mm} \textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperClique-Decompositions, Cancer&#39;s Neutrosophic Recognition &nbsp;&nbsp; \\ \textbf{AMS Subject Classification:} 05C17, 05C22, 05E45 \section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research} In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer&#39;s attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer&#39;s attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups&#39;&#39;. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I&#39;ve found the SuperHyperModels which are officially called ``SuperHyperGraphs&#39;&#39; and ``Neutrosophic SuperHyperGraphs&#39;&#39;. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices&#39;&#39; and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges&#39;&#39;. Thus it&#39;s another motivation for us to do research on this SuperHyperModel based on the ``Cancer&#39;s Recognition&#39;&#39;. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it&#39;s the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It&#39;s SuperHyperModel. It&#39;s SuperHyperGraph but it&#39;s officially called ``Neutrosophic SuperHyperGraphs&#39;&#39;. The cancer is the disease but the model is going to figure out what&#39;s going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognition&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances&#39; styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.&nbsp; The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it&#39;s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. There are some specific models, which are well-known and they&#39;ve got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath (-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the optimal&nbsp;&nbsp; SuperHyperClique-Decompositions or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic SuperHyperPath s have only two SuperHyperEdges but it&#39;s not enough since it&#39;s essential to have at least three SuperHyperEdges to form any style of a SuperHyperClique-Decompositions. There isn&#39;t any formation of any SuperHyperClique-Decompositions but literarily, it&#39;s the deformation of any SuperHyperClique-Decompositions. It, literarily, deforms and it doesn&#39;t form. \begin{question} How to define the SuperHyperNotions and to do research on them to find the `` amount of&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; based on the fixed groups of cells or the fixed groups of group of cells? \end{question} \begin{question} What are the best descriptions for the ``Cancer&#39;s Recognition&#39;&#39; in terms of these messy and dense SuperHyperModels where embedded notions are illustrated? \end{question} It&#39;s motivation to find notions to use in this dense model is titled ``SuperHyperGraphs&#39;&#39;. Thus it motivates us to define different types of ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39; on ``SuperHyperGraph&#39;&#39; and ``Neutrosophic SuperHyperGraph&#39;&#39;. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer&#39;s Recognition&#39;&#39;, more understandable and more clear. \\ The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries&#39;&#39;, initial definitions about SuperHyperGraphs and Neutrosophic SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what&#39;s going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,&nbsp;&nbsp; SuperHyperClique-Decompositions and Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions, are figured out in sections ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; and ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39;. In the sense of tackling on getting results and in Clique-Decompositions to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what&#39;s done in this section, titled ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results&#39;&#39;. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results&#39;&#39;, ``&nbsp; SuperHyperClique-Decompositions&#39;&#39;, ``Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions&#39;&#39;, ``Results on SuperHyperClasses&#39;&#39; and ``Results on Neutrosophic SuperHyperClasses&#39;&#39;. There are curious questions about what&#39;s done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best&#39;&#39; as the description and adjective for this research as presented in section, ``&nbsp; SuperHyperClique-Decompositions&#39;&#39;. The keyword of this research debut in the section ``Applications in Cancer&#39;s Recognition&#39;&#39; with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel&#39;&#39; and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel&#39;&#39;. In the section, ``Open Problems&#39;&#39;, there are some scrutiny and discernment on what&#39;s done and what&#39;s happened in this research in the terms of ``questions&#39;&#39; and ``problems&#39;&#39; to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what&#39;s done in this research to make sense&nbsp; and to get sense about what&#39;s figured out are included in the section, ``Conclusion and Closing Remarks&#39;&#39;. \section{Neutrosophic Preliminaries Of This Scientific Research On the Redeemed Ways} In this section, the basic material in this scientific research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}. \\ In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited. \begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\ &nbsp;Let $X$ be a Clique-Decompositions of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form $$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\ &nbsp;Let $X$ be a Clique-Decompositions of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as &nbsp;$$A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;);$&nbsp; &nbsp; \item[$(ix)$] and the following conditions hold: $$T&#39;_V(E_{i&#39;})\leq\min[T_{V&#39;}(V_i),T_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ I&#39;_V(E_{i&#39;})\leq\min[I_{V&#39;}(V_i),I_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}},$$ $$ \text{and}~F&#39;_V(E_{i&#39;})\leq\min[F_{V&#39;}(V_i),F_{V&#39;}(V_j)]_{V_i,V_j\in E_{i&#39;}}$$ where $i&#39;=1,2,\ldots,n&#39;.$ \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\ &nbsp;A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w&nbsp; \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set&nbsp; $A = \{&lt; x:T_A(x),I_A(x),F_A(x)&gt;, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)&gt; 0\}.$$ \end{definition} \begin{definition}(General Forms of&nbsp; Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V&#39;$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$ is a pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V&#39;;$ \item[$(ii)$] $V=\{(V_i,T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)):~T_{V&#39;}(V_i),I_{V&#39;}(V_i),F_{V&#39;}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n&#39;}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i&#39;},T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})):~T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;})\geq0\},~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i&#39;}\neq\emptyset,~(i&#39;=1,2,\ldots,n&#39;);$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i&#39;}supp(E_{i&#39;})=V,~(i&#39;=1,2,\ldots,n&#39;).$&nbsp; &nbsp; \end{itemize} Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V&#39;}(V_i),I_{V&#39;}(V_i),$ and $F_{V&#39;}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T&#39;_{V}(E_{i&#39;}),T&#39;_{V}(E_{i&#39;}),$ and $T&#39;_{V}(E_{i&#39;})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i&#39;}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii&#39;$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T&#39;_{V}(E_{i&#39;}),I&#39;_{V}(E_{i&#39;}),F&#39;_{V}(E_{i&#39;}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i&#39;}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i&#39;},$ $|V_i|=1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{HyperEdge}; \item[$(v)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|=2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there&#39;s a $V_i$ is incident in $E_{i&#39;}$ such that $|V_i|\geq1,$ and $|E_{i&#39;}|\geq2,$&nbsp; then $E_{i&#39;}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there&#39;s a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} &nbsp;A graph is \textbf{SuperHyperUniform} if it&#39;s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable. \begin{definition} &nbsp;Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} &nbsp;\item[(i).] It&#39;s \textbf{Neutrosophic SuperHyperPath } if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; &nbsp;\item[(ii).] it&#39;s \textbf{SuperHyperCycle} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges; &nbsp; \item[(iii).] it&#39;s \textbf{SuperHyperStar} it&#39;s only one SuperVertex as intersection amid all SuperHyperEdges; &nbsp;&nbsp; \item[(iv).] it&#39;s \textbf{SuperHyperBipartite} it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp; \item[(v).] it&#39;s \textbf{SuperHyperMultiPartite}&nbsp; it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; &nbsp;&nbsp;&nbsp;&nbsp; \item[(vi).] it&#39;s \textbf{SuperHyperWheel} if it&#39;s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} &nbsp;Let a pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ &nbsp; is called a \textbf{Neutrosophic&nbsp; SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex&nbsp; (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: &nbsp; \begin{itemize} &nbsp;\item[$(i)$]&nbsp; $V_i,V_{i+1}\in E_{i&#39;};$ &nbsp;\item[$(ii)$]&nbsp;&nbsp; there&#39;s a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(iii)$]&nbsp; there&#39;s a SuperVertex $V&#39;_i \in V_i$ such that $V&#39;_i,V_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(iv)$]&nbsp;&nbsp; there&#39;s a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(v)$]&nbsp; there&#39;s a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp;&nbsp; \item[$(vi)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(vii)$]&nbsp;&nbsp; there are a vertex $v_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $v_i,V&#39;_{i+1}\in E_{i&#39;};$ &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(viii)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V&#39;_i,v_{i+1}\in E_{i&#39;};$ &nbsp; \item[$(ix)$]&nbsp;&nbsp; there are a SuperVertex $V&#39;_i\in V_i$ and a SuperVertex $V&#39;_{i+1} \in V_{i+1}$ such that $V&#39;_i,V&#39;_{i+1}\in E_{i&#39;}.$ &nbsp; \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic&nbsp; SuperHyperPaths).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ a Neutrosophic&nbsp; SuperHyperPath&nbsp; (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} &nbsp;\item[$(i)$] If for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j&#39;},$ $|E_{j&#39;}|=2,$&nbsp; and there&#39;s $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j&#39;},$ $|V_i|=1,~|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j&#39;},$ $|V_i|\geq1,|E_{j&#39;}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE) &nbsp;$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ have \begin{itemize} &nbsp;\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$; \item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$ \item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$ \item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$ \end{itemize} \end{definition} \begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a&nbsp; pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp; \item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$ \item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$ \end{itemize} \end{definition} &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic e-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic re-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall E&#39;_a,E&#39;_b: E&#39;_a,E&#39;_b \text{are Clique}; \end{eqnarray*} and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperClique-Decompositions} if the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperClique-Decompositions} f the following expression is called \textbf{Neutrosophic v-SuperHyperClique-Decompositions criteria} holds &nbsp; \begin{eqnarray*} &amp;&amp; \forall V&#39;_a,V&#39;_b: V&#39;_a,V&#39;_b \text{are Clique}; \end{eqnarray*} and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme V-SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic V-SuperHyperClique-Decompositions} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; &nbsp;\item[$(vii)$] an \textbf{Extreme V-SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperClique-Decompositions; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperClique-Decompositions SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperClique-Decompositions, Neutrosophic re-SuperHyperClique-Decompositions, Neutrosophic v-SuperHyperClique-Decompositions, and Neutrosophic rv-SuperHyperClique-Decompositions and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperClique-Decompositions; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((Extreme/Neutrosophic)$\delta-$SuperHyperClique-Decompositions).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; Then \begin{itemize} &nbsp;\item[$(i)$] an \textbf{$\delta-$SuperHyperClique-Decompositions} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Decompositions such that either of the following expressions hold for the Neutrosophic cardinalities of&nbsp; SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)| &gt; |S\cap (V\setminus N(s))|+\delta; \label{136EQN1} &nbsp;\\&amp;&amp; |S\cap N(s)| &lt; |S\cap (V\setminus N(s))|+\delta. \label{136EQN2} \end{eqnarray*} The Expression \eqref{136EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive}; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperClique-Decompositions} is a Neutrosophic kind of Neutrosophic SuperHyperClique-Decompositions such that either of the following Neutrosophic expressions hold for the Neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray*} &amp;&amp;|S\cap N(s)|_{Neutrosophic} &gt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{136EQN3} &nbsp;\\&amp;&amp; |S\cap N(s)|_{Neutrosophic} &lt; |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{136EQN4} \end{eqnarray*} The Expression \eqref{136EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{136EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the notion of ``Neutrosophic SuperHyperGraph&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$&nbsp; It&#39;s redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{136TBL3} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL3} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of SuperHyperClasses. Since there&#39;s more ways to get Neutrosophic type-results to make a Neutrosophic more understandable. \begin{definition}\label{136DEF2} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{136TBL4} holds. Thus&nbsp; Neutrosophic SuperHyperPath ,&nbsp; SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and&nbsp;&nbsp; SuperHyperWheel, are &nbsp;\textbf{Neutrosophic SuperHyperPath},&nbsp; \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{136TBL4} holds. &nbsp;\begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{136DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL4} \end{table} \end{definition} It&#39;s useful to define a ``Neutrosophic&#39;&#39; version of a Neutrosophic SuperHyperClique-Decompositions. Since there&#39;s more ways to get type-results to make a Neutrosophic SuperHyperClique-Decompositions more Neutrosophicly understandable. \\ For the sake of having a Neutrosophic SuperHyperClique-Decompositions, there&#39;s a need to ``\textbf{redefine}&#39;&#39; the Neutrosophic notion of ``Neutrosophic SuperHyperClique-Decompositions&#39;&#39;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&#39;s the usage of the position of labels to assign to the values. \begin{definition}\label{136DEF1} &nbsp;Assume a SuperHyperClique-Decompositions. It&#39;s redefined a \textbf{Neutrosophic SuperHyperClique-Decompositions} if the Table \eqref{136TBL1} holds.&nbsp; \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{136DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBL1} \end{table} \end{definition} \section{ Neutrosophic SuperHyperClique-Decompositions But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Neutrosophic event).\\ &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Any Neutrosophic k-subset of $A$ of $V$ is called \textbf{Neutrosophic k-event} and if $k=2,$ then Neutrosophic subset of $A$ of $V$ is called \textbf{Neutrosophic event}. The following expression is called \textbf{Neutrosophic probability} of $A.$ \begin{eqnarray} &nbsp;E(A)=\sum_{a\in A}E(a). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Independent).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. $s$ Neutrosophic k-events $A_i,~i\in I$ is called \textbf{Neutrosophic s-independent} if the following expression is called \textbf{Neutrosophic s-independent criteria} \begin{eqnarray*} &nbsp;E(\cap_{i\in I}A_i)=\prod_{i\in I}P(A_i). \end{eqnarray*} And if $s=2,$ then Neutrosophic k-events of $A$ and $B$ is called \textbf{Neutrosophic independent}. The following expression is called \textbf{Neutrosophic independent criteria} \begin{eqnarray} &nbsp;E(A\cap B)=P(A)P(B). \end{eqnarray} \end{definition} \begin{definition}(Neutrosophic Variable).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Any k-function Clique-Decompositions like $E$ is called \textbf{Neutrosophic k-Variable}. If $k=2$, then any 2-function Clique-Decompositions like $E$ is called \textbf{Neutrosophic Variable}. \end{definition} The notion of independent on Neutrosophic Variable is likewise. \begin{definition}(Neutrosophic Expectation).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Expectation} if the following expression is called \textbf{Neutrosophic Expectation criteria} \begin{eqnarray*} &nbsp;Ex(E)=\sum_{\alpha \in V}E(\alpha)P(\alpha). \end{eqnarray*} \end{definition} \begin{definition}(Neutrosophic Crossing).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Neutrosophic number is called \textbf{Neutrosophic Crossing} if the following expression is called \textbf{Neutrosophic Crossing criteria} \begin{eqnarray*} &nbsp;Cr(S)=\min\{\text{Number of Crossing in a Plane Embedding of } S\}. \end{eqnarray*} \end{definition} \begin{lemma} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $m$ and $n$ propose special Clique-Decompositions. Then with $m\geq 4n,$ \end{lemma} \begin{proof} &nbsp;Consider a planar embedding $G$ of $G$ with $cr(G)$ crossings. Let $S$ be a Neutrosophic&nbsp; random k-subset of $V$ obtained by choosing each SuperHyperVertex of $G$ Neutrosophic independently with probability Clique-Decompositions $p := 4n/m,$ and set $H:=G[S]$ and $H:=G[S].$ &nbsp;\\ Define random variables $X, Y, Z$ on $V$ as follows: $X$ is the Neutrosophic number of SuperHyperVertices, $Y$ the Neutrosophic number of SuperHyperEdges, and $Z$ the Neutrosophic number of crossings of $H.$ The trivial bound noted above, when applied to $H,$ yields the inequality $Z &ge; cr(H) &ge; Y -3X.$ By linearity of Neutrosophic Expectation, $$E(Z) &ge; E(Y )-3E(X).$$ Now $E(X) = pn,~E(Y ) = p^2m$ (each SuperHyperEdge having some SuperHyperEnds) and $E(Z) = p^4cr(G)$ (each crossing being defined by some SuperHyperVertices). Hence $$p^4cr(G) &ge; p^2m-3pn.$$ Dividing both sides by $p^4,$ we have: &nbsp;\begin{eqnarray*} cr(G)\geq \frac{pm-3n}{p^3}=\frac{n}{{(4n/m)}^3}=\frac{1}{64}{m^3}{n^2}. \end{eqnarray*} \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $l$ be the Neutrosophic number of SuperHyperLines in the plane passing through at least $k+1$ of these points, where $1 \leq k \leq 2 \sqrt{2n}.$ Then $l&lt;32n^2/k^3.$ \end{theorem} \begin{proof} Form a Neutrosophic SuperHyperGraph $G$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdge are the segments between consecutive points on the SuperHyperLines which pass through at least $k+1$ points of $P.$ This Neutrosophic SuperHyperGraph has at least $kl$ SuperHyperEdges and Neutrosophic crossing at most 􏰈$l$ choose two. Thus either $kl &lt; 4n,$ in which case $l &lt; 4n/k \leq32n^2/k^3,$ or $l^2/2 &gt; \text{l choose 2} \geq cr(G) \geq {(kl)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and again $l &lt; 32n^2/k^3. \end{proof} \begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a SuperHyperSet of $n$ points in the plane, and let $k$ be the number of pairs of points of $P$ at unit SuperHyperDistance. Then $k &lt; 5n^{4/3}.$ \end{theorem} \begin{proof} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Draw a SuperHyperUnit SuperHyperCircle around each SuperHyperPoint of $P.$ Let $n_i$ be the Neutrosophic number of these SuperHyperCircles passing through exactly $i$ points of $P.$ Then&nbsp; $\sum{i=0}^{􏰄n-1}n_i = n$ and $k = \frac{1}{2}􏰄\sum{i=0}^{􏰄n-1}in_i.$ Now form a Neutrosophic SuperHyperGraph $H$ with SuperHyperVertex SuperHyperSet $P$ whose SuperHyperEdges are the SuperHyperArcs between consecutive SuperHyperPoints on the SuperHyperCircles that pass through at least three SuperHyperPoints of $P.$ Then &nbsp;\begin{eqnarray*} e(H)=\sum_{i=3}^{n-1}in_i=2k-n_1-2n_2\geq2k-2n. \end{eqnarray*} Some SuperHyperPairs of SuperHyperVertices of $H$ might be joined by some parallel SuperHyperEdges. Delete from $H$ one of each SuperHyperPair of parallel SuperHyperEdges, so as to obtain a simple Neutrosophic SuperHyperGraph $G$ with $e(G) &ge; k-n.$ Now $cr(G) &le; n(n-1)$ because $G$ is formed from at most n SuperHyperCircles, and any two SuperHyperCircles cross at most twice. Thus either $e(G) &lt; 4n,$ in which case $k &lt; 5n &lt; 5n^{4/3},$ or $n^2 &gt; n(n-1) &ge; cr(G) &ge; {(k-n)}^3/64n^2$ by the Neutrosophic Crossing Lemma, and $k&lt;4n^{4/3} +n&lt;5n^{4/3}.$ \end{proof} \begin{proposition} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a nonnegative Neutrosophic Variable and t a positive real number. Then &nbsp; \begin{eqnarray*} P(X\geq t) \leq \frac{E(X)}{t}. \end{eqnarray*} \end{proposition} &nbsp;\begin{proof} &nbsp;&nbsp; \begin{eqnarray*} &amp;&amp; E(X)=\sum \{X(a)P(a):a\in V\} \geq \sum\{X(a)P(a):a\in V,X(a)\geq t\} 􏰅􏰅 \\&amp;&amp; \sum\{tP(a):a\in V,X(a)\geq t\} 􏰅􏰅=t\sum\{P(a):a\in V,X(a)\geq t\} \\&amp;&amp; tP(X\geq t). \end{eqnarray*} Dividing the first and last members by $t$ yields the asserted inequality. \end{proof} &nbsp;\begin{corollary} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X_n$ be a nonnegative integer-valued variable in a prob- ability Clique-Decompositions $(V_n,E_n), n\geq1.$ If $E(X_n)\rightarrow0$ as $n\rightarrow \infty,$ then $P(X_n =0)\rightarrow1$ as $n \rightarrow \infty.$ \end{corollary} &nbsp;\begin{proof} \end{proof} &nbsp;\begin{theorem} &nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. &nbsp;A special SuperHyperGraph in $G_{n,p}$ almost surely has stability number at most $\lceil2p^{-1} \log n\rceil.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. &nbsp;A special SuperHyperGraph in $G_{n,p}$ is up. Let $G\in \mathcal{G}_{n,p}$&nbsp; and let $S$ be a given SuperHyperSet of $k+1$ SuperHyperVertices of $G,$ where $k\in \Bbb N.$ The probability that $S$ is a stable SuperHyperSet of $G$ is $(1-p)^{(k+1) \text{choose} 2},$ this being the probability that none of the $(k+1) \text{choose} 2$ pairs of SuperHyperVertices of $S$ is a SuperHyperEdge of the Neutrosophic SuperHyperGraph $G.$ &nbsp;\\ Let $A_S$ denote the event that $S$ is a stable SuperHyperSet of $G,$ and let $X_S$ denote the indicator Neutrosophic Variable for this Neutrosophic Event. By equation, we have &nbsp; \begin{eqnarray*} E(X_S) = P(X_S = 1) = P(A_S ) = (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} Let $X$ be the number of stable SuperHyperSets of cardinality $k + 1$ in $G.$ Then 􏰄 &nbsp; \begin{eqnarray*} X = \sum\{X_S : S \subseteq V, |S| = k + 1\} \end{eqnarray*} and so, by those, 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)= \sum\{E(X_S): S\subseteq V, |S|=k+1}= (\text{n choose k+1})&nbsp; (1-p)^{(k+1) \text{choose} 2}. \end{eqnarray*} We bound the right-hand side by invoking two elementary inequalities: 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} (\text{n choose k+1})\leq \frac{n^{k+1}}{(k+1)!} \text{and} 1-p&le;e^{-p}. \end{eqnarray*} This yields the following upper bound on $E(X).$ &nbsp; 􏰄􏰉􏰊&nbsp; \begin{eqnarray*} E(X)\leq\frac{n^{k+1}e^{-p)(k+1) \text{choose} 2}}{(k+1)!}=\frac{􏰇ne^{-pk/2}^{􏰈k+1}}{(k+1)!} \end{eqnarray*} Suppose now that $k = \lceil2p^{-1} \log n\rceil.$ Then $k &ge; 2p^{-1} \log n,$ so $ne^{-pk/2} \leq 1.$&nbsp;&nbsp; Because $k$ grows at least as fast as the logarithm of $n,$&nbsp; implies that $E(X) \rightarrow 0$ as $n \rightarrow \infty.$ Because $X$ is integer-valued and nonnegative, we deduce from Corollary that $P (X = 0) \rightarrow 1$ as $n \rightarrow \infty.$ Consequently, a Neutrosophic SuperHyperGraph in $\mathcal{G}_{n,p}$ almost surely has stability number at most $k.$ \end{proof} \begin{definition}(Neutrosophic Variance).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. A Neutrosophic k-Variable $E$ has a number is called \textbf{Neutrosophic Variance} if the following expression is called \textbf{Neutrosophic Variance criteria} \begin{eqnarray*} &nbsp;Vx(E)=Ex({(X-Ex(X))}^2). \end{eqnarray*} \end{definition} &nbsp;\begin{theorem} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)\leq \frac{V(X)}{t^2}. \end{eqnarray*} &nbsp; \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X$ be a Neutrosophic Variable and let $t$ be a positive real number. Then &nbsp;\begin{eqnarray*} E(|X-Ex(X)|\geq t)=E{((X-Ex(X))}^2 \geq t^2)\leq \frac{Ex({(X-Ex(X))}^2)}{t^2}=\frac{V(X)}{t^2}. 􏱫 \end{eqnarray*} &nbsp; \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $X_n$ be a Neutrosophic Variable in a probability Clique-Decompositions (V_n , E_n ), n \geq 1.$ If $Ex(X_n)\neq 0$ and $V(X_n) &lt;&lt; E^2(X_n),$ then &nbsp;&nbsp;&nbsp; \begin{eqnarray*} E(X_n=0)\rightarrow 0~\text{as}~n\rightarrow \infty \end{eqnarray*} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Set $X := X_n$ and $t := |Ex(X_n)|$ in Chebyshev&rsquo;s Inequality, and observe that $E (X_n = 0) \leq E (|X_n - Ex(X_n)| \geq |Ex(X_n)|)$ because $|X_n - Ex(X_n)| = |Ex(X_n)|$ when $X_n = 0.$ \end{proof} \begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $G \in \mathcal{G}_{n,1/2}.$ For $0 \leq k \leq n,$ set $f(k) := \text{(n choose k)}􏰇􏰈2^{-\text{(k choose 2)}}$ and let $k^{*}$ be the least value of $k$ for which $f(k)$ is less than one. Then almost surely $\alpha(G)$ takes one of the three values $k^{*}-2,k^{*}-1,k^{*}.$ \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. As in the proof of related Theorem, the result is straightforward. \end{proof} \begin{corollary} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $G \in \mathcal{G}_{n,1/2}$ and let $f$ and $k^{*}$ be as defined in previous Theorem. Then either: &nbsp;&nbsp; \begin{itemize} &nbsp;\item[$(i).$] $f(k^{*}) &lt;&lt; 1,$ in which case almost surely $\alpha(G)$ is equal to either&nbsp; $k^{*}-2$ or&nbsp; $k^{*}-1$, or &nbsp;\item[$(ii).$] $f(k^{*}-1) &gt;&gt; 1,$ in which case almost surely $\alpha(G)$&nbsp; is equal to either $k^{*}-1$ or $k^{*}.$ \end{itemize} \end{corollary} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. The latter is straightforward. \end{proof} \begin{definition}(Neutrosophic Threshold).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $P$ be a&nbsp; monotone property of SuperHyperGraphs (one which is preserved when SuperHyperEdges are added). Then a \textbf{Neutrosophic Threshold} for $P$ is a function $f(n)$ such that: &nbsp;\begin{itemize} &nbsp;\item[$(i).$]&nbsp; if $p &lt;&lt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely does not have $P,$ &nbsp;\item[$(ii).$]&nbsp; if $p &gt;&gt; f(n),$ then $G \in \mathcal{G}_{n,p}$ almost surely has $P.$ \end{itemize} \end{definition} \begin{definition}(Neutrosophic Balanced).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $F$ be a fixed Neutrosophic SuperHyperGraph. Then there is a threshold function for the property of containing a copy of $F$ as a Neutrosophic SubSuperHyperGraph is called \textbf{Neutrosophic Balanced}. \end{definition} &nbsp;\begin{theorem} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. Let $F$ be a nonempty balanced Neutrosophic SubSuperHyperGraph with $k$ SuperHyperVertices and $l$ SuperHyperEdges. Then $n^{-k/l}$ is a threshold function for the property of containing $F$ as a Neutrosophic SubSuperHyperGraph. \end{theorem} &nbsp;\begin{proof} &nbsp;&nbsp; Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider $S=(V,E)$ is a probability Clique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Decompositions. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG1} \end{figure} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperClique-Decompositions. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG2} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}=\{\{E_4\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1\},\{V_2\},\{V_3\},\{V_1,V_2\},\{V_1,V_4\},\{V_2,V_4\},\{V_i\}_{i\neq3}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG3.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG3} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =\{\{E_4\},\{E_5\},\{E_1,E_4\},\{E_1,E_5\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}}=2z^2. &nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_1,V_2,V_3,N,F,V_4\}.\{V_1,V_2,V_3,N,F,H\},\{V_1,V_2,V_3,N,F,O\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =3z^6. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG4.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG4} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\}_{i\neq j\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; &nbsp;=(\text{Four Choose Two})z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{i=1}^5,\{V_i\}_{i=5}^8,\dots\} &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=2z^5+2z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG5.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG5} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{E_1,E_2\},\ldots\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp; \\&amp;&amp; &nbsp; =\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =bz. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG6.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG6} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_i,E_{13},E_{14},E_{16}\}_{i=3}^7,\ldots\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =2z^8+z^7. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{V_i,V_{13}\}_{i=4}^7,\ldots\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG7.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG7} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_i\}_{i=1}^4. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp; =z^4. \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{V_{13},V_i\}_{i=4}^7,\{V_{14},V_i\}_{i=8}^{11},\{V_{12},V_i\}_{i=1}^3,\{V_i\}_{i=12}^{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG8.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG8} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{E_i,E_{i+1}\}_{i=1}^{10}\}. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; =az^2. &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp; =\{\{V_i,V_{i+1}\}_{i=1}^{10},\{V_i,V_{22}\}_{i=11}^{20}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =az^2+z^{11}. &nbsp;&nbsp;&nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG9.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG9} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{E_1,E_4,E_5,E_6,\{E_4,E_5,E_6\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^1+z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}}= &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_{13},V_i\}_{i=4}^7,\{V_{14},V_i\}_{i=8}^{11},\{V_{12},V_i\}_{i=1}^3,\{V_i\}_{i=12}^{14}\}. &nbsp;\\&amp;&amp; &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; =2z^5+z^4+z^3. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG10.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG10} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_2,E_3,E_4,E_5\},\{E_2,E_4,E_5\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^4+z^3+az^2+7z. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{\{V_4,V_5,V_6\},\{V_1,V_2,V_3\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3+az^2+6z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG11.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG11} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}=\{E_1,\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;&nbsp; \\&amp;&amp; &nbsp;=az^2+6z. &nbsp;\\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{V_1,V_2,V_3,V_7,V_8\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; =z^5+az^2+10z. \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG12.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG12} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}}= &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \{\{E_2,E_3,E_4,E_5\},\{E_2,E_4,E_5\},\{E_1,E_9,E_{10}\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp;\\&amp;&amp;&nbsp; &nbsp; &nbsp;=z^4+2z^3+az^2+10z. &nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; =\{\{V_4,V_5,V_6\},\{V_1,V_2,V_3\},\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;\\&amp;&amp; &nbsp;=2z^3+az^2+6z. \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG13.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG13} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}}=\{\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}}= 2z^2+3z. &nbsp;\end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG14.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG14} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; =5z^2+6z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG15.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG15} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG16.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG16} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG17.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG17} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=4z^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{i=8}^{17},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;&nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG18.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG18} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+12z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_8},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{9}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG19.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG19} &nbsp;\end{figure} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_6},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =az^{b}+\ldots+kz. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG20.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{136NSHG20} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^2+2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_2},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{10}+\ldots+10z. &nbsp; \end{eqnarray*} &nbsp;\begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG1.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG1} &nbsp;\end{figure} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperClique-Decompositions, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2,E_3\},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=z^3+az^2+5z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_3},\ldots,\{V_i,V_j\},\{V_k\}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp; =z^{12}+\ldots+az. &nbsp; \end{eqnarray*} &nbsp; \begin{figure} &nbsp;\includegraphics[width=100mm]{95NHG2.png} &nbsp; &nbsp;&nbsp; \caption{The Neutrosophic SuperHyperGraphs Associated to the Neutrosophic Notions of Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM1} } &nbsp;\label{95NHG2} &nbsp;\end{figure} \end{itemize} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \end{proposition} \begin{proposition} Assume a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Decompositions minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Decompositions, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \end{proposition} \begin{proposition} Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Decompositions is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Decompositions is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Decompositions in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Decompositions. \end{proposition} \begin{proposition} &nbsp;Assume a simple Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then the Neutrosophic number of&nbsp; type-result-R-Clique-Decompositions has, the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality, is the Neutrosophic cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E&#39;},c_{E&#39;&#39;},c_{E&#39;&#39;&#39;}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ If there&#39;s a Neutrosophic type-result-R-Clique-Decompositions with the least Neutrosophic cardinality, the lower sharp Neutrosophic bound for cardinality. \end{proposition} \begin{proposition} &nbsp;Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=z^5. \end{eqnarray*} Is a Neutrosophic type-result-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic type-result-Clique-Decompositions is the cardinality of \begin{eqnarray*} &nbsp;&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial}=z^4. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions}=\{V_1,V_2,V_3,V_4,V_1\}. \\&amp;&amp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=z^5. \end{eqnarray*} \end{proposition} \begin{proof} Assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The SuperHyperSet of the SuperHyperVertices $V\setminus V\setminus \{z\}$ isn&#39;t a quasi-R-Clique-Decompositions since neither amount of Neutrosophic SuperHyperEdges nor amount of SuperHyperVertices where amount refers to the Neutrosophic number of SuperHyperVertices(-/SuperHyperEdges) more than one to form any kind of SuperHyperEdges or any number of SuperHyperEdges. Let us consider the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ This Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices has the eligibilities to propose property such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices but the maximum Neutrosophic cardinality indicates that these Neutrosophic&nbsp; type-SuperHyperSets couldn&#39;t give us the Neutrosophic lower bound in the term of Neutrosophic sharpness. In other words, the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ of the Neutrosophic SuperHyperVertices implies at least on-quasi-triangle style is up but sometimes the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ &nbsp;of the Neutrosophic SuperHyperVertices is free-quasi-triangle and it doesn&#39;t make a contradiction to the supposition on the connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Thus the minimum case never happens in the generality of the connected loopless Neutrosophic SuperHyperGraphs. Thus if we assume in the worst case, literally, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a quasi-R-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a&nbsp; quasi-R-Clique-Decompositions is the cardinality of $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;Then we&#39;ve lost some connected loopless Neutrosophic SuperHyperClasses of the connected loopless Neutrosophic SuperHyperGraphs titled free-triangle, on-triangle, and their quasi-types but the SuperHyperStable is only up in this quasi-R-Clique-Decompositions. It&#39;s the contradiction to that fact on the generality. There are some counterexamples to deny this statement. One of them comes from the setting of the graph titled path and cycle as the counterexamples-classes or reversely direction star as the examples-classes, are well-known classes in that setting and they could be considered as the examples-classes and counterexamples-classes for the tight bound of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; Let $V\setminus V\setminus \{z\}$ in mind. There&#39;s no necessity on the SuperHyperEdge since we need at least two SuperHyperVertices to form a SuperHyperEdge. It doesn&#39;t withdraw the principles of the main definition since there&#39;s no condition to be satisfied but the condition is on the existence of the SuperHyperEdge instead of acting on the SuperHyperVertices. In other words, if there&#39;s a SuperHyperEdge, then the Neutrosophic SuperHyperSet has the necessary condition for the intended definition to be applied. Thus the $V\setminus V\setminus \{z\}$ is withdrawn not by the conditions of the main definition but by the necessity of the pre-condition on the usage of the main definition. &nbsp; \\ &nbsp; The Neutrosophic structure of the Neutrosophic R-Clique-Decompositions decorates the Neutrosophic SuperHyperVertices don&#39;t have received any Neutrosophic connections so as this Neutrosophic style implies different versions of Neutrosophic SuperHyperEdges with the maximum Neutrosophic cardinality in the terms of Neutrosophic SuperHyperVertices are spotlight. The lower Neutrosophic bound is to have the maximum Neutrosophic groups of Neutrosophic SuperHyperVertices have perfect Neutrosophic connections inside each of SuperHyperEdges and the outside of this Neutrosophic SuperHyperSet doesn&#39;t matter but regarding the connectedness of the used Neutrosophic SuperHyperGraph arising from its Neutrosophic properties taken from the fact that it&#39;s simple. If there&#39;s no more than one Neutrosophic SuperHyperVertex in the targeted Neutrosophic SuperHyperSet, then there&#39;s no Neutrosophic connection. Furthermore, the Neutrosophic existence of one Neutrosophic SuperHyperVertex has no&nbsp; Neutrosophic effect to talk about the Neutrosophic R-Clique-Decompositions. Since at least two Neutrosophic SuperHyperVertices involve to make a title in the Neutrosophic background of the Neutrosophic SuperHyperGraph. The Neutrosophic SuperHyperGraph is obvious if it has no Neutrosophic SuperHyperEdge but at least two Neutrosophic SuperHyperVertices make the Neutrosophic version of Neutrosophic SuperHyperEdge. Thus in the Neutrosophic setting of non-obvious Neutrosophic SuperHyperGraph, there are at least one Neutrosophic SuperHyperEdge. It&#39;s necessary to mention that the word ``Simple&#39;&#39; is used as Neutrosophic adjective for the initial Neutrosophic SuperHyperGraph, induces there&#39;s no Neutrosophic&nbsp; appearance of the loop Neutrosophic version of the Neutrosophic SuperHyperEdge and this Neutrosophic SuperHyperGraph is said to be loopless. The Neutrosophic adjective ``loop&#39;&#39; on the basic Neutrosophic framework engages one Neutrosophic SuperHyperVertex but it never happens in this Neutrosophic setting. With these Neutrosophic bases, on a Neutrosophic SuperHyperGraph, there&#39;s at least one Neutrosophic SuperHyperEdge thus there&#39;s at least a Neutrosophic R-Clique-Decompositions has the Neutrosophic cardinality of a Neutrosophic SuperHyperEdge. Thus, a Neutrosophic R-Clique-Decompositions has the Neutrosophic cardinality at least a Neutrosophic SuperHyperEdge. Assume a Neutrosophic SuperHyperSet $V\setminus V\setminus \{z\}.$ This Neutrosophic SuperHyperSet isn&#39;t a Neutrosophic R-Clique-Decompositions since either the Neutrosophic SuperHyperGraph is an obvious Neutrosophic SuperHyperModel thus it never happens since there&#39;s no Neutrosophic usage of this Neutrosophic framework and even more there&#39;s no Neutrosophic connection inside or the Neutrosophic SuperHyperGraph isn&#39;t obvious and as its consequences, there&#39;s a Neutrosophic contradiction with the term ``Neutrosophic R-Clique-Decompositions&#39;&#39; since the maximum Neutrosophic cardinality never happens for this Neutrosophic style of the Neutrosophic SuperHyperSet and beyond that there&#39;s no Neutrosophic connection inside as mentioned in first Neutrosophic case in the forms of drawback for this selected Neutrosophic SuperHyperSet. Let $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Comes up. This Neutrosophic case implies having the Neutrosophic style of on-quasi-triangle Neutrosophic style on the every Neutrosophic elements of this Neutrosophic SuperHyperSet. Precisely, the Neutrosophic R-Clique-Decompositions is the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that some Neutrosophic amount of the Neutrosophic SuperHyperVertices are on-quasi-triangle Neutrosophic style. The Neutrosophic cardinality of the v SuperHypeSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots,a_{E&#39;},b_{E&#39;},c_{E&#39;},\ldots\right\}_{E,E&#39;=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}$$ Is the maximum in comparison to the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But the lower Neutrosophic bound is up. Thus the minimum Neutrosophic cardinality of the maximum Neutrosophic cardinality ends up the Neutrosophic discussion. The first Neutrosophic term refers to the Neutrosophic setting of the Neutrosophic SuperHyperGraph but this key point is enough since there&#39;s a Neutrosophic SuperHyperClass of a Neutrosophic SuperHyperGraph has no on-quasi-triangle Neutrosophic style amid some amount of its Neutrosophic SuperHyperVertices. This Neutrosophic setting of the Neutrosophic SuperHyperModel proposes a Neutrosophic SuperHyperSet has only some amount&nbsp; Neutrosophic SuperHyperVertices from one Neutrosophic SuperHyperEdge such that there&#39;s no Neutrosophic amount of Neutrosophic SuperHyperEdges more than one involving these some amount of these Neutrosophic SuperHyperVertices. The Neutrosophic cardinality of this Neutrosophic SuperHyperSet is the maximum and the Neutrosophic case is occurred in the minimum Neutrosophic situation. To sum them up, the Neutrosophic SuperHyperSet &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Has the maximum Neutrosophic cardinality such that $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Contains some Neutrosophic SuperHyperVertices such that there&#39;s distinct-covers-order-amount Neutrosophic SuperHyperEdges for amount of Neutrosophic SuperHyperVertices taken from the Neutrosophic SuperHyperSet $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;It means that the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices &nbsp; $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is a Neutrosophic&nbsp; R-Clique-Decompositions for the Neutrosophic SuperHyperGraph as used Neutrosophic background in the Neutrosophic terms of worst Neutrosophic case and the common theme of the lower Neutrosophic bound occurred in the specific Neutrosophic SuperHyperClasses of the Neutrosophic SuperHyperGraphs which are Neutrosophic free-quasi-triangle. &nbsp; \\ Assume a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$&nbsp; Neutrosophic number of the Neutrosophic SuperHyperVertices. Then every Neutrosophic SuperHyperVertex has at least no Neutrosophic SuperHyperEdge with others in common. Thus those Neutrosophic SuperHyperVertices have the eligibles to be contained in a Neutrosophic R-Clique-Decompositions. Those Neutrosophic SuperHyperVertices are potentially included in a Neutrosophic&nbsp; style-R-Clique-Decompositions. Formally, consider $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ Are the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z.$$ where the $\sim$ isn&#39;t an equivalence relation but only the symmetric relation on the Neutrosophic&nbsp; SuperHyperVertices of the Neutrosophic SuperHyperGraph. The formal definition is as follows. $$Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z$$ if and only if $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices and there&#39;s only and only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ between the Neutrosophic SuperHyperVertices $Z_i$ and $Z_j.$ The other definition for the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ in the terms of Neutrosophic R-Clique-Decompositions is $$\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}.$$ This definition coincides with the definition of the Neutrosophic R-Clique-Decompositions but with slightly differences in the maximum Neutrosophic cardinality amid those Neutrosophic type-SuperHyperSets of the Neutrosophic SuperHyperVertices. Thus the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$\max_z|\{Z_1,Z_2,\ldots,Z_z~|~Z_i\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}|_{\text{Neutrosophic cardinality}},$$ and $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ is formalized with mathematical literatures on the Neutrosophic R-Clique-Decompositions. Let $Z_i\overset E\sim Z_j,$ be defined as $Z_i$ and $Z_j$ are the Neutrosophic SuperHyperVertices belong to the Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}.$ Thus, &nbsp; $$E=\{Z_1,Z_2,\ldots,Z_z~|~Z_i\overset E\sim Z_j,~i\neq j,~ i,j=1,2,\ldots,z\}.$$ Or $$\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ But with the slightly differences, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Decompositions}= &nbsp;\\&amp;&amp; &nbsp;\{Z_1,Z_2,\ldots,Z_z~|~\forall i\neq j,~ i,j=1,2,\ldots,z,~\exists E_x,~Z_i\overset{E_x}\sim Z_j,\}. \end{eqnarray*} \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;\text{Neutrosophic R-Clique-Decompositions}= &nbsp;\\&amp;&amp; V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}. \end{eqnarray*} Thus $E\in E_{ESHG:(V,E)}$ is a Neutrosophic quasi-R-Clique-Decompositions where $E\in E_{ESHG:(V,E)}$ is fixed that means $E_x=E\in E_{ESHG:(V,E)}.$ for all Neutrosophic intended SuperHyperVertices but in a Neutrosophic Clique-Decompositions, $E_x=E\in E_{ESHG:(V,E)}$ could be different and it&#39;s not unique. To sum them up, in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ If a Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has $z$ Neutrosophic SuperHyperVertices, then the Neutrosophic cardinality of the Neutrosophic R-Clique-Decompositions is at least $$V\setminus (V\setminus\left\{a_{E},b_{E},c_{E},\ldots,z_{E}\right\}).$$ &nbsp;It&#39;s straightforward that&nbsp; the Neutrosophic cardinality of the Neutrosophic R-Clique-Decompositions is at least the maximum Neutrosophic number of Neutrosophic SuperHyperVertices of the Neutrosophic SuperHyperEdges with the maximum number of the Neutrosophic SuperHyperEdges. In other words, the maximum number of the Neutrosophic SuperHyperEdges contains the maximum Neutrosophic number of Neutrosophic SuperHyperVertices are renamed to Neutrosophic Clique-Decompositions in some cases but the maximum number of the&nbsp; Neutrosophic SuperHyperEdge with the maximum Neutrosophic number of Neutrosophic SuperHyperVertices, has the Neutrosophic SuperHyperVertices are contained in a Neutrosophic R-Clique-Decompositions. \\ The obvious SuperHyperGraph has no Neutrosophic SuperHyperEdges. But the non-obvious Neutrosophic SuperHyperModel is up. The quasi-SuperHyperModel addresses some issues about the Neutrosophic optimal SuperHyperObject. It specially delivers some remarks on the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices such that there&#39;s distinct amount of Neutrosophic SuperHyperEdges for distinct amount of Neutrosophic SuperHyperVertices up to all&nbsp; taken from that Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices but this Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices is either has the maximum Neutrosophic SuperHyperCardinality or it doesn&#39;t have&nbsp; maximum Neutrosophic SuperHyperCardinality. In a non-obvious SuperHyperModel, there&#39;s at least one Neutrosophic SuperHyperEdge containing at least all Neutrosophic SuperHyperVertices. Thus it forms a Neutrosophic quasi-R-Clique-Decompositions where the Neutrosophic completion of the Neutrosophic incidence is up in that.&nbsp; Thus it&#39;s, literarily, a Neutrosophic embedded R-Clique-Decompositions. The SuperHyperNotions of embedded SuperHyperSet and quasi-SuperHyperSet coincide. In the original setting, these types of SuperHyperSets only don&#39;t satisfy on the maximum SuperHyperCardinality. Thus the embedded setting is elected such that those SuperHyperSets have the maximum Neutrosophic SuperHyperCardinality and they&#39;re Neutrosophic SuperHyperOptimal. The less than two distinct types of Neutrosophic SuperHyperVertices are included in the minimum Neutrosophic style of the embedded Neutrosophic R-Clique-Decompositions. The interior types of the Neutrosophic SuperHyperVertices are deciders. Since the Neutrosophic number of SuperHyperNeighbors are only&nbsp; affected by the interior Neutrosophic SuperHyperVertices. The common connections, more precise and more formal, the perfect unique connections inside the Neutrosophic SuperHyperSet for any distinct types of Neutrosophic SuperHyperVertices pose the Neutrosophic R-Clique-Decompositions. Thus Neutrosophic exterior SuperHyperVertices could be used only in one Neutrosophic SuperHyperEdge and in Neutrosophic SuperHyperRelation with the interior Neutrosophic SuperHyperVertices in that&nbsp; Neutrosophic SuperHyperEdge. In the embedded Neutrosophic Clique-Decompositions, there&#39;s the usage of exterior Neutrosophic SuperHyperVertices since they&#39;ve more connections inside more than outside. Thus the title ``exterior&#39;&#39; is more relevant than the title ``interior&#39;&#39;. One Neutrosophic SuperHyperVertex has no connection, inside. Thus, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices with one SuperHyperElement has been ignored in the exploring to lead on the optimal case implying the Neutrosophic R-Clique-Decompositions. The Neutrosophic R-Clique-Decompositions with the exclusion of the exclusion of all&nbsp; Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge and with other terms, the Neutrosophic R-Clique-Decompositions with the inclusion of all Neutrosophic SuperHyperVertices in one Neutrosophic SuperHyperEdge, is a Neutrosophic quasi-R-Clique-Decompositions. To sum them up, in a connected non-obvious Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ There&#39;s only one&nbsp; Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only the maximum possibilities of the distinct interior Neutrosophic SuperHyperVertices inside of any given Neutrosophic quasi-R-Clique-Decompositions minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. In other words, there&#39;s only an unique Neutrosophic SuperHyperEdge $E\in E_{ESHG:(V,E)}$ has only two distinct Neutrosophic SuperHyperVertices in an&nbsp; Neutrosophic quasi-R-Clique-Decompositions, minus all&nbsp; Neutrosophic SuperHypeNeighbor to some of them but not all of them. \\ The main definition of the Neutrosophic R-Clique-Decompositions has two titles. a Neutrosophic quasi-R-Clique-Decompositions and its corresponded quasi-maximum Neutrosophic R-SuperHyperCardinality are two titles in the terms of quasi-R-styles. For any Neutrosophic number, there&#39;s a Neutrosophic quasi-R-Clique-Decompositions with that quasi-maximum Neutrosophic SuperHyperCardinality in the terms of the embedded Neutrosophic SuperHyperGraph. If there&#39;s an embedded Neutrosophic SuperHyperGraph, then the Neutrosophic quasi-SuperHyperNotions lead us to take the collection of all the Neutrosophic quasi-R-Clique-Decompositionss for all Neutrosophic numbers less than its Neutrosophic corresponded maximum number. The essence of the Neutrosophic Clique-Decompositions ends up but this essence starts up in the terms of the Neutrosophic quasi-R-Clique-Decompositions, again and more in the operations of collecting all the Neutrosophic quasi-R-Clique-Decompositionss acted on the all possible used formations of the Neutrosophic SuperHyperGraph to achieve one Neutrosophic number. This Neutrosophic number is\\ considered as the equivalence class for all corresponded quasi-R-Clique-Decompositionss. Let $z_{\text{Neutrosophic Number}},S_{\text{Neutrosophic SuperHyperSet}}$ and $G_{\text{Neutrosophic Clique-Decompositions}}$ be a Neutrosophic number, a Neutrosophic SuperHyperSet and a Neutrosophic Clique-Decompositions. Then \begin{eqnarray*} &amp;&amp;[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}=\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} As its consequences, the formal definition of the Neutrosophic Clique-Decompositions is re-formalized and redefined as follows. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} To get more precise perceptions, the follow-up expressions propose another formal technical definition for the Neutrosophic Clique-Decompositions. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} In more concise and more convenient ways, the modified definition for the Neutrosophic Clique-Decompositions poses the upcoming expressions. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} To translate the statement to this mathematical literature, the&nbsp; formulae will be revised. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} And then, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}}\\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} To get more visions in the closer look-up, there&#39;s an overall overlook. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{S_{\text{Neutrosophic SuperHyperSet}}~| \\&amp;&amp;~S_{\text{Neutrosophic SuperHyperSet}}=G_{\text{Neutrosophic Clique-Decompositions}}, \\&amp;&amp;~|S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{S\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |S_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Now, the extension of these types of approaches is up. Since the new term, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;, could be redefined as the collection of the Neutrosophic SuperHyperVertices such that any amount of its Neutrosophic SuperHyperVertices are incident to a Neutrosophic&nbsp; SuperHyperEdge. It&#39;s, literarily,&nbsp; another name for ``Neutrosophic&nbsp; Quasi-Clique-Decompositions&#39;&#39; but, precisely, it&#39;s the generalization of&nbsp; ``Neutrosophic&nbsp; Quasi-Clique-Decompositions&#39;&#39; since ``Neutrosophic Quasi-Clique-Decompositions&#39;&#39; happens ``Neutrosophic Clique-Decompositions&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and background but ``Neutrosophic SuperHyperNeighborhood&#39;&#39; may not happens ``Neutrosophic Clique-Decompositions&#39;&#39; in a Neutrosophic SuperHyperGraph as initial framework and preliminarily background since there are some ambiguities about the Neutrosophic SuperHyperCardinality arise from it. To get orderly keywords, the terms, ``Neutrosophic SuperHyperNeighborhood&#39;&#39;,&nbsp; ``Neutrosophic Quasi-Clique-Decompositions&#39;&#39;, and&nbsp; ``Neutrosophic Clique-Decompositions&#39;&#39; are up. \\ Thus, let $z_{\text{Neutrosophic Number}},N_{\text{Neutrosophic SuperHyperNeighborhood}}$ and $G_{\text{Neutrosophic Clique-Decompositions}}$ be a Neutrosophic number, a Neutrosophic SuperHyperNeighborhood and a Neutrosophic Clique-Decompositions and the new terms are up. \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}}\}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \}. \end{eqnarray*} And with go back to initial structure, \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}\in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}= \\&amp;&amp; \cup_{z_{\text{Neutrosophic Number}}}\{N_{\text{Neutrosophic SuperHyperNeighborhood}}~| \\&amp;&amp;~|N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp;=z_{\text{Neutrosophic Number}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperNeighborhood}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max_{[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}}z_{\text{Neutrosophic Number}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} \begin{eqnarray*} &amp;&amp;G_{\text{Neutrosophic Clique-Decompositions}}= \\&amp;&amp; \{N_{\text{Neutrosophic SuperHyperNeighborhood}} \\&amp;&amp; \in\cup_{z_{\text{Neutrosophic Number}}}[z_{\text{Neutrosophic Number}}]_{\text{Neutrosophic Class}}~|~ \\&amp;&amp; |N_{\text{Neutrosophic SuperHyperSet}}|_{\text{Neutrosophic Cardinality}} \\&amp;&amp; =\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\} \}. \end{eqnarray*} Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ &nbsp; To make sense with the precise words in the terms of ``R-&#39;, the follow-up illustrations are coming up. &nbsp; \\ &nbsp; The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperVertices is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Decompositions. &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic R-Clique-Decompositions. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp; &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is an \underline{\textbf{Neutrosophic R-Clique-Decompositions}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge amid some Neutrosophic SuperHyperVertices instead of all given by \underline{\textbf{Neutrosophic Clique-Decompositions}} is related to the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; There&#39;s&nbsp;&nbsp; \underline{not} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Decompositions is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Decompositions is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{one}} Neutrosophic SuperHyperVertex. But the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; doesn&#39;t have less than two&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet since they&#39;ve come from at least so far an SuperHyperEdge. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Decompositions \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of Neutrosophic SuperHyperVertices, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; \underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Decompositions. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices, &nbsp;$$(V\setminus V\setminus \{x,z\})\cup\{xy\}$$ or $$(V\setminus V\setminus \{x,z\})\cup\{zy\}$$ &nbsp;&nbsp; is an&nbsp; Neutrosophic R-Clique-Decompositions $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Decompositions \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Decompositions}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic SuperHyperEdge for some amount Neutrosophic&nbsp; SuperHyperVertices instead of all given by that Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Decompositions. There isn&#39;t&nbsp; only less than two Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;&nbsp; Thus the non-obvious&nbsp; Neutrosophic R-Clique-Decompositions, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; is up. The non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Decompositions, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ Is&nbsp; the Neutrosophic SuperHyperSet, not: $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;does includes only less than two SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E)$ but it&#39;s impossible in the case, they&#39;ve corresponded to an SuperHyperEdge. It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; R-Clique-Decompositions&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic R-Clique-Decompositions}}, \end{center} &nbsp;is only and only $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E)$&nbsp; with a illustrated SuperHyperModeling. It&#39;s also, not only a Neutrosophic free-triangle embedded SuperHyperModel and a Neutrosophic on-triangle embedded SuperHyperModel but also it&#39;s a Neutrosophic stable embedded SuperHyperModel. But all only non-obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic&nbsp; R-Clique-Decompositions amid those obvious simple Neutrosophic type-SuperHyperSets of the Neutrosophic Clique-Decompositions, are $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ \\ To sum them up,&nbsp; assume a connected loopless Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally, $$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp;is a Neutrosophic R-Clique-Decompositions. In other words, the least cardinality, the lower sharp bound for the cardinality, of a Neutrosophic&nbsp; R-Clique-Decompositions is the cardinality of &nbsp;$$V\setminus V\setminus\left\{a_{E},b_{E},c_{E},\ldots\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$ &nbsp; \\ To sum them up,&nbsp; in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The all interior Neutrosophic SuperHyperVertices belong to any Neutrosophic quasi-R-Clique-Decompositions if for any of them, and any of other corresponded Neutrosophic SuperHyperVertex, some interior Neutrosophic SuperHyperVertices are mutually Neutrosophic&nbsp; SuperHyperNeighbors with no Neutrosophic exception at all minus&nbsp; all Neutrosophic SuperHypeNeighbors to any amount of them. \\ Assume a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ Let a Neutrosophic SuperHyperEdge $ESHE: E\in E_{ESHG:(V,E)}$ has some Neutrosophic SuperHyperVertices $r.$ Consider all Neutrosophic numbers of those Neutrosophic SuperHyperVertices from that Neutrosophic SuperHyperEdge excluding excluding more than $r$ distinct Neutrosophic SuperHyperVertices, exclude to any given Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices. Consider there&#39;s a Neutrosophic&nbsp; R-Clique-Decompositions with the least cardinality, the lower sharp Neutrosophic bound for Neutrosophic cardinality. Assume a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $ V_{ESHE}\setminus \{z\}$ is a Neutrosophic SuperHyperSet $S$ of&nbsp; the Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have&nbsp; some Neutrosophic SuperHyperVertices uniquely but it isn&#39;t a Neutrosophic R-Clique-Decompositions. Since it doesn&#39;t have&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices such that there&#39;s a Neutrosophic SuperHyperEdge to have some SuperHyperVertices uniquely. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE}\cup \{z\}$ is the maximum Neutrosophic cardinality of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices but it isn&#39;t a Neutrosophic R-Clique-Decompositions. Since it \textbf{\underline{doesn&#39;t do}} the Neutrosophic procedure such that such that there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic&nbsp; SuperHyperVertices uniquely&nbsp; [there are at least one Neutrosophic SuperHyperVertex outside&nbsp; implying there&#39;s, sometimes in&nbsp; the connected Neutrosophic SuperHyperGraph $ESHG:(V,E),$ a Neutrosophic SuperHyperVertex, titled its Neutrosophic SuperHyperNeighbor,&nbsp; to that Neutrosophic SuperHyperVertex in the Neutrosophic SuperHyperSet $S$ so as $S$ doesn&#39;t do ``the Neutrosophic procedure&#39;&#39;.]. There&#39;s&nbsp; only \textbf{\underline{one}} Neutrosophic SuperHyperVertex&nbsp;&nbsp;&nbsp; \textbf{\underline{outside}} the intended Neutrosophic SuperHyperSet, $V_{ESHE}\cup \{z\},$ in the terms of Neutrosophic SuperHyperNeighborhood. Thus the obvious Neutrosophic R-Clique-Decompositions,&nbsp; $V_{ESHE}$ is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic R-Clique-Decompositions,&nbsp; $V_{ESHE},$ \textbf{\underline{is}} a Neutrosophic SuperHyperSet, $V_{ESHE},$&nbsp; \textbf{\underline{includes}} only \textbf{\underline{all}}&nbsp; Neutrosophic SuperHyperVertices does forms any kind of Neutrosophic pairs are titled&nbsp;&nbsp; \underline{Neutrosophic SuperHyperNeighbors} in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperVertices $V_{ESHE},$ is the \textbf{\underline{maximum Neutrosophic SuperHyperCardinality}} of a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperVertices&nbsp; \textbf{\underline{such that}}&nbsp; there&#39;s a Neutrosophic SuperHyperEdge to have some Neutrosophic SuperHyperVertices uniquely. Thus, in a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ Any Neutrosophic R-Clique-Decompositions only contains all interior Neutrosophic SuperHyperVertices and all exterior Neutrosophic SuperHyperVertices from the unique Neutrosophic SuperHyperEdge where there&#39;s any of them has all possible&nbsp; Neutrosophic SuperHyperNeighbors in and there&#39;s all&nbsp; Neutrosophic SuperHyperNeighborhoods in with no exception minus all&nbsp; Neutrosophic SuperHypeNeighbors to some of them not all of them&nbsp; but everything is possible about Neutrosophic SuperHyperNeighborhoods and Neutrosophic SuperHyperNeighbors out. \\ The SuperHyperNotion, namely,&nbsp; Clique-Decompositions, is up.&nbsp; There&#39;s neither empty SuperHyperEdge nor loop SuperHyperEdge. The following Neutrosophic SuperHyperSet&nbsp; of Neutrosophic&nbsp; SuperHyperEdges[SuperHyperVertices] is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Decompositions. &nbsp;The Neutrosophic SuperHyperSet of Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp; is the simple Neutrosophic type-SuperHyperSet of the Neutrosophic Clique-Decompositions. The Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an \underline{\textbf{Neutrosophic Clique-Decompositions}} $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a Neutrosophic&nbsp; type-SuperHyperSet with \underline{\textbf{the maximum Neutrosophic cardinality}}&nbsp; of a Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There are&nbsp;&nbsp;&nbsp; \underline{not} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious&nbsp; Neutrosophic Clique-Decompositions is up. The obvious simple Neutrosophic type-SuperHyperSet called the&nbsp; Neutrosophic Clique-Decompositions is a Neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} Neutrosophic SuperHyperVertices. But the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Doesn&#39;t have less than three&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended Neutrosophic SuperHyperSet. Thus the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Decompositions \underline{\textbf{is}} up. To sum them up, the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Decompositions. Since the Neutrosophic SuperHyperSet of the Neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is an&nbsp; Neutrosophic Clique-Decompositions $\mathcal{C}(ESHG)$ for an&nbsp; Neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the Neutrosophic SuperHyperSet $S$ of Neutrosophic SuperHyperVertices such that there&#39;s no a Neutrosophic&nbsp; SuperHyperEdge for some&nbsp; Neutrosophic SuperHyperVertices given by that Neutrosophic type-SuperHyperSet&nbsp; called the&nbsp; Neutrosophic Clique-Decompositions \underline{\textbf{and}} it&#39;s an&nbsp; Neutrosophic \underline{\textbf{ Clique-Decompositions}}. Since it\underline{\textbf{&#39;s}}&nbsp;&nbsp; \underline{\textbf{the maximum Neutrosophic cardinality}} of&nbsp; a Neutrosophic SuperHyperSet $S$ of&nbsp; Neutrosophic SuperHyperEdges[SuperHyperVertices] such that there&#39;s no&nbsp; Neutrosophic SuperHyperVertex of a Neutrosophic SuperHyperEdge is common and there&#39;s an&nbsp;&nbsp; Neutrosophic SuperHyperEdge for all Neutrosophic SuperHyperVertices. There aren&#39;t&nbsp; only less than three Neutrosophic&nbsp; SuperHyperVertices \underline{\textbf{inside}} the intended&nbsp; Neutrosophic SuperHyperSet, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;Thus the non-obvious&nbsp; Neutrosophic Clique-Decompositions, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is up. The obvious simple Neutrosophic type-SuperHyperSet of the&nbsp; Neutrosophic Clique-Decompositions, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Is&nbsp; the Neutrosophic SuperHyperSet, not: \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected Neutrosophic&nbsp; SuperHyperGraph $ESHG:(V,E).$ It&#39;s interesting to mention that the only non-obvious simple Neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``Neutrosophic&nbsp; Clique-Decompositions&#39;&#39;}} \end{center} &nbsp;amid those obvious[non-obvious] simple Neutrosophic type-SuperHyperSets called the \begin{center} &nbsp;\underline{\textbf{Neutrosophic Clique-Decompositions}}, \end{center} &nbsp;is only and only \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{Neutrosophic Quasi-Clique-Decompositions SuperHyperPolynomial} &nbsp; \\&amp;&amp;=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{Neutrosophic R-Quasi-Clique-Decompositions SuperHyperPolynomial}=az^{s}+bz^{t}. \end{eqnarray*} &nbsp;In a connected Neutrosophic SuperHyperGraph $ESHG:(V,E).$ &nbsp;\end{proof} \section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|-1)z^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG18.png} \caption{a Neutrosophic SuperHyperPath Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Example \eqref{136EXM18a}} \label{136NSHG18a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=(|E_{NSHG}|)z^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}},E_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp;&nbsp; \\&amp;&amp;E_{\frac{|E_{NSHG}|}{3}},V^{EXTERNAL}_{\frac{|E_{NSHG}|}{3}} &nbsp;\end{eqnarray*} &nbsp; be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG19.png} \caption{a Neutrosophic SuperHyperCycle Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM19a}} \label{136NSHG19a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;CENTER,E_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,CENTER &nbsp;\end{eqnarray*} be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG20.png} \caption{a Neutrosophic SuperHyperStar Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM20a}} \label{136NSHG20a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}+z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp; is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. Then there&#39;s no at least one SuperHyperClique-Decompositions. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Decompositions taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG21.png} \caption{Neutrosophic SuperHyperBipartite Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Example \eqref{136EXM21a}} \label{136NSHG21a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_1,E_2\}_{i=1}^{|P^{\max}_{NSHG}|},\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in P_i\in\{P_a~|~ |P_a|=\max |P_b|_{P_b\in P_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |P_b|_{P_b\in P_{NSHG}}~}+z^{\max |E_b|_{E_b\in E_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|}. &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E_2,V^{EXTERNAL}_2, &nbsp; \\&amp;&amp;\ldots, &nbsp; \\&amp;&amp;E_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|},V^{EXTERNAL}_{|P_i|=\min_{P_j\in E_{NSHG}}|P_j|} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperClique-Decompositions taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperClique-Decompositions. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG22.png} \caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Example \eqref{136EXM22a}} \label{136NSHG22a} \end{figure} \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{E_i,E_j\},\{E_k\}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Clique-Decompositions SuperHyperPolynomial}} &nbsp; \\&amp;&amp; &nbsp;=az^2+(|E_{NSHG}|)z. &nbsp;\\&amp;&amp; &nbsp; &nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-Clique-Decompositions}} &nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =\{\{V^{EXTERNAL}_i\}_{V^{EXTERNAL}_i\in E^{*}_i\in\{E^{*}_a~|~ |E^{*}_a|=\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~\}},\{V_i\}_{V_i\in E_c},\ldots,\{V_i,V_j\},\{V_k\}\}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic V-Clique-Decompositions SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; &nbsp;=z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}++z^{\max |E^{*}_b|_{E^{*}_b\in E^{*}_{NSHG}}~}+\ldots+az. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;CENTER,E^{*}_2 &nbsp;\end{eqnarray*} &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;E^{*}_1,V^{EXTERNAL}_1, &nbsp;\\&amp;&amp;E^{*}_2,CENTER &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperClique-Decompositions taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperClique-Decompositions. The latter is straightforward. Then there&#39;s at least one SuperHyperClique-Decompositions. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperClique-Decompositions could be applied. The unique embedded SuperHyperClique-Decompositions proposes some longest SuperHyperClique-Decompositions excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperClique-Decompositions. \begin{figure} \includegraphics[width=100mm]{136NSHG23.png} \caption{a Neutrosophic SuperHyperWheel Neutrosophic Associated to the Neutrosophic Notions of&nbsp; Neutrosophic SuperHyperClique-Decompositions in the Neutrosophic Example \eqref{136EXM23a}} \label{136NSHG23a} \end{figure} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation} For the SuperHyperClique-Decompositions,&nbsp; Neutrosophic SuperHyperClique-Decompositions, and the Neutrosophic SuperHyperClique-Decompositions, some general results are introduced. \begin{remark} &nbsp;Let remind that the Neutrosophic SuperHyperClique-Decompositions is ``redefined&#39;&#39; on the positions of the alphabets. \end{remark} \begin{corollary} &nbsp;Assume Neutrosophic SuperHyperClique-Decompositions. Then &nbsp;\begin{eqnarray*} &amp;&amp; Neutrosophic ~SuperHyperClique-Decompositions=\\&amp;&amp;\{the&nbsp;&nbsp; SuperHyperClique-Decompositions of the SuperHyperVertices ~|~\\&amp;&amp;\max|SuperHyperOffensive \\&amp;&amp;SuperHyperClique-Decompositions \\&amp;&amp; |_{Neutrosophic cardinality amid those SuperHyperClique-Decompositions.}\} &nbsp; \end{eqnarray*} plus one Neutrosophic SuperHypeNeighbor to one. Where $\sigma_i$ is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for $i=1,2,3,$ respectively. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then the notion of Neutrosophic SuperHyperClique-Decompositions and SuperHyperClique-Decompositions coincide. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a Neutrosophic SuperHyperClique-Decompositions if and only if it&#39;s a SuperHyperClique-Decompositions. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then a consecutive sequence of the SuperHyperVertices is a strongest SuperHyperClique-Decompositions if and only if it&#39;s a longest SuperHyperClique-Decompositions. \end{corollary} \begin{corollary} Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Decompositions is its SuperHyperClique-Decompositions and reversely. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel) on the same identical letter of the alphabet. Then its Neutrosophic SuperHyperClique-Decompositions is its SuperHyperClique-Decompositions and reversely. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Decompositions isn&#39;t well-defined if and only if its SuperHyperClique-Decompositions isn&#39;t well-defined. \end{corollary} \begin{corollary} &nbsp;Assume a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} \begin{corollary} &nbsp;Assume SuperHyperClasses of a Neutrosophic SuperHyperGraph. Then its Neutrosophic SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} \begin{corollary} Assume a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). Then its Neutrosophic SuperHyperClique-Decompositions is well-defined if and only if its SuperHyperClique-Decompositions is well-defined. \end{corollary} % \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $V$ is \begin{itemize} &nbsp;\item[$(i):$]&nbsp; the dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $NTG:(V,E,\sigma,\mu)$&nbsp; be a Neutrosophic SuperHyperGraph. Then $\emptyset$ is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected defensive SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph. Then an independent SuperHyperSet is \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; the strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Decompositions/SuperHyperPath. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-SuperHyperDefensive SuperHyperClique-Decompositions; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperUniform SuperHyperWheel. Then $V$ is a maximal \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG)$-dual SuperHyperDefensive SuperHyperClique-Decompositions; \end{itemize} Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperClique-Decompositions/SuperHyperPath. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] the SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the connected SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperWheel. Then the number of \begin{itemize} &nbsp;\item[$(i):$] the dual SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] the dual&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; the dual connected SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; the dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; the strong dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; the connected dual $\mathcal{O}(ESHG)$-SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $V.$ Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices is a \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then a SuperHyperSet contains the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices in the biggest SuperHyperPart is a \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\delta$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperUniform SuperHyperGraph which is a SuperHyperStar/SuperHyperComplete SuperHyperBipartite/SuperHyperComplete SuperHyperMultipartite. Then Then the number of \begin{itemize} &nbsp;\item[$(i):$] dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$]&nbsp; connected dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\frac{\mathcal{O}(ESHG)}{2}+1$-dual SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} is one and it&#39;s only $S,$ a SuperHyperSet contains [the SuperHyperCenter and] the half of multiplying $r$ with the number of all the SuperHyperEdges plus one of all the SuperHyperVertices. Where the exterior SuperHyperVertices and the interior SuperHyperVertices coincide. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. The number of connected component is $|V-S|$ if there&#39;s a SuperHyperSet which is a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong 1-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected 1-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph. Then the number is at most $\mathcal{O}(ESHG)$ and&nbsp; the Neutrosophic number is at most $\mathcal{O}_n(ESHG).$ \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. The number is $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] &nbsp;SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$] strong &nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is $\emptyset.$ The number is&nbsp; $0$ and&nbsp; the Neutrosophic number is $0,$ for an independent SuperHyperSet in the setting of dual \begin{itemize} &nbsp;\item[$(i):$] SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $0$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $0$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $0$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperComplete. Then there&#39;s no independent SuperHyperSet. \end{proposition} \begin{proposition} Let $ESHG:(V,E)$ be a Neutrosophic SuperHyperGraph which is SuperHyperClique-Decompositions/SuperHyperPath/SuperHyperWheel. The number is&nbsp; $\mathcal{O}(ESHG:(V,E))$ and&nbsp; the Neutrosophic number is $\mathcal{O}_n(ESHG:(V,E)),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $\mathcal{O}(ESHG:(V,E))$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} Let $ESHG:(V,E)$&nbsp; be a Neutrosophic SuperHyperGraph which is SuperHyperStar/complete SuperHyperBipartite/complete SuperHyperMultiPartite. The number is&nbsp; $\frac{\mathcal{O}(ESHG:(V,E))}{2}+1$ and&nbsp; the Neutrosophic number is $\min\Sigma_{v\in\{v_1,v_2,\cdots,v_t\}_{t&gt;\frac{\mathcal{O}(ESHG:(V,E))}{2}}\subseteq V}\sigma(v),$ in the setting of a dual \begin{itemize} &nbsp;\item[$(i):$]&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii):$]&nbsp; strong&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp; \item[$(iii):$] connected&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv):$]&nbsp; $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(v):$]&nbsp; strong $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \item[$(vi):$]&nbsp; connected $(\frac{\mathcal{O}(ESHG:(V,E))}{2}+1)$-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;Let $\mathcal{NSHF}:(V,E)$ be a SuperHyperFamily of the $ESHGs:(V,E)$ Neutrosophic SuperHyperGraphs which are from one-type SuperHyperClass which the result is obtained for the individuals. Then the results also hold for the SuperHyperFamily $\mathcal{NSHF}:(V,E)$ of these specific SuperHyperClasses of the&nbsp; Neutrosophic SuperHyperGraphs. \end{proposition} % \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions, then $\forall v\in V\setminus S,~\exists x\in S$ such that &nbsp;&nbsp; \begin{itemize} \item[$(i)$] $v\in N_s(x);$ \item[$(ii)$] $vx\in E.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. If $S$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions, then &nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $S$ is SuperHyperClique-Decompositions set; \item[$(ii)$] there&#39;s $S\subseteq S&#39;$ such that $|S&#39;|$ is SuperHyperChromatic number. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O};$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n.$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph which is connected. Then &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \begin{itemize} \item[$(i)$] $\Gamma\leq\mathcal{O}-1;$ \item[$(ii)$] $\Gamma_s\leq\mathcal{O}_n-\Sigma_{i=1}^{3}\sigma_i(x).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperPath. Then &nbsp;\begin{itemize} \item[$(i)$] the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperClique-Decompositions. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperClique-Decompositions. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is&nbsp; a&nbsp; dual&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] &nbsp;$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$; \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$ \item[$(iv)$] the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperStar. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c\}$ is&nbsp; a dual maximal SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=1;$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$ \item[$(iv)$] the SuperHyperSets $S=\{c\}$ and $S\subset S&#39;$ are only dual SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be SuperHyperWheel. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$ \item[$(iii)$] $\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$ \item[$(iv)$] the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an odd SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual&nbsp; SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $ESHG:(V,E)$&nbsp; be an even SuperHyperComplete. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperClique-Decompositions; \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor;$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$ \item[$(iv)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of Neutrosophic SuperHyperStars with common Neutrosophic SuperHyperVertex SuperHyperSet. Then &nbsp;\begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=m$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S&#39;$ are only dual&nbsp; SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is&nbsp; a dual maximal SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF};$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp; Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common Neutrosophic SuperHyperVertex SuperHyperSet. Then \begin{itemize} \item[$(i)$] the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is&nbsp; a dual SuperHyperDefensive SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E);$ \item[$(ii)$] $\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$ \item[$(iii)$] $\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$ \item[$(iv)$] the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual&nbsp; maximal SuperHyperClique-Decompositions for $\mathcal{NSHF}:(V,E).$ \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is an s-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is a dual s-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a strong Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $s\geq t+2$ and a SuperHyperSet $S$ of SuperHyperVertices is an t-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions, then $S$ is an s-SuperHyperPowerful&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$] if $s\leq t$ and a SuperHyperSet $S$ of SuperHyperVertices is a dual t-SuperHyperDefensive SuperHyperClique-Decompositions, then $S$ is a dual s-SuperHyperPowerful&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$&nbsp; be a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an V-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual V-SuperHyperDefensive SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an V-SuperHyperDefensive SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual V-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a&nbsp; SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Decompositions. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|&lt; 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} \begin{proposition} &nbsp;&nbsp; Let $ESHG:(V,E)$ is a[an] [V-]SuperHyperUniform-strong-Neutrosophic SuperHyperGraph which is SuperHyperClique-Decompositions. Then following statements hold; \begin{itemize} &nbsp;\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|&lt; 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp; \item[$(ii)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap S|&gt; 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp; \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions; &nbsp;&nbsp;&nbsp;&nbsp; \item[$(iv)$]&nbsp; if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive&nbsp; SuperHyperClique-Decompositions. \end{itemize} \end{proposition} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\section{Neutrosophic Applications in Cancer&#39;s Neutrosophic Recognition} The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what&#39;s going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease. \\ In the following, some Neutrosophic steps are Neutrosophic devised on this disease. \begin{description} &nbsp;\item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function. &nbsp; \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it&#39;s called Neutrosophic SuperHyperGraph] and the long Neutrosophic cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn&#39;t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it&#39;s said to be Neutrosophic SuperHyperGraph] to have convenient perception on what&#39;s happened and what&#39;s done. &nbsp;\item[Step 3. (Neutrosophic Model)] &nbsp; There are some specific Neutrosophic models, which are well-known and they&#39;ve got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperClique-Decompositions, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,&nbsp; SuperHyperWheel). The aim is to find either the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions or the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions in those Neutrosophic Neutrosophic SuperHyperModels. &nbsp; \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as&nbsp; Neutrosophic SuperHyperModel} &nbsp;\item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa21aa}, the Neutrosophic SuperHyperBipartite is Neutrosophic highlighted and Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG21.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperBipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Decompositions} &nbsp;\label{136NSHGaa21aa} \end{figure} \\ By using the Neutrosophic Figure \eqref{136NSHGaa21aa} and the Table \eqref{136TBLaa21aa}, the Neutrosophic SuperHyperBipartite is obtained. \\ The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa21aa}, is the Neutrosophic SuperHyperClique-Decompositions. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperBipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa21aa} \end{table} &nbsp;&nbsp;&nbsp; \section{Case 2: The Increasing Neutrosophic Steps Toward Neutrosophic SuperHyperMultipartite as Neutrosophic SuperHyperModel} &nbsp;&nbsp;&nbsp;&nbsp; \item[Step 4. (Neutrosophic Solution)] In the Neutrosophic Figure \eqref{136NSHGaa22aa}, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and&nbsp; Neutrosophic featured. \begin{figure} &nbsp;\includegraphics[width=100mm]{136NSHG22.png} &nbsp;\caption{a Neutrosophic&nbsp; SuperHyperMultipartite Associated to the Notions of&nbsp;&nbsp; Neutrosophic SuperHyperClique-Decompositions} &nbsp;\label{136NSHGaa22aa} \end{figure} \\ &nbsp;By using the Neutrosophic Figure \eqref{136NSHGaa22aa} and the Table \eqref{136TBLaa22aa}, the Neutrosophic SuperHyperMultipartite is obtained. &nbsp;\\ &nbsp;The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHGaa22aa}, is the&nbsp; Neutrosophic SuperHyperClique-Decompositions. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperMultipartite} \begin{tabular}[t]{c|c} \hline The Values of The Vertices &amp; The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&amp;The maximum Values of Its Vertices\\ \hline The Values of The Edges&amp;The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&amp;The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&amp;The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{136TBLaa22aa} \end{table} &nbsp;&nbsp;&nbsp;&nbsp; \end{description} \section{Wondering Open Problems But As The Directions To Forming The Motivations} In what follows, some ``problems&#39;&#39; and some ``questions&#39;&#39; are proposed. \\ The&nbsp;&nbsp; SuperHyperClique-Decompositions and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions are defined on a real-world application, titled ``Cancer&#39;s Recognitions&#39;&#39;. \begin{question} Which the else SuperHyperModels could be defined based on Cancer&#39;s recognitions? \end{question} \begin{question} Are there some SuperHyperNotions related to&nbsp;&nbsp; SuperHyperClique-Decompositions and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions? \end{question} \begin{question} Are there some Algorithms to be defined on the SuperHyperModels to compute them? \end{question} \begin{question} Which the SuperHyperNotions are related to beyond the&nbsp;&nbsp; SuperHyperClique-Decompositions and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions? \end{question} \begin{problem} The&nbsp;&nbsp; SuperHyperClique-Decompositions and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions do a SuperHyperModel for the Cancer&#39;s recognitions and they&#39;re based on&nbsp;&nbsp; SuperHyperClique-Decompositions, are there else? \end{problem} \begin{problem} Which the fundamental SuperHyperNumbers are related to these SuperHyperNumbers types-results? \end{problem} \begin{problem} What&#39;s the independent research based on Cancer&#39;s recognitions concerning the multiple types of SuperHyperNotions? \end{problem} \section{Conclusion and&nbsp; Closing Remarks} In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted. \\ This research uses some approaches to make Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the&nbsp;&nbsp; SuperHyperClique-Decompositions. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it&#39;s mentioned on the title ``Cancer&#39;s Recognitions&#39;&#39;. To formalize the instances on the SuperHyperNotion,&nbsp;&nbsp; SuperHyperClique-Decompositions, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the&nbsp;&nbsp; SuperHyperClique-Decompositions and the Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Neutrosophic SuperHyperGraph are the SuperHyperModels on the ``Cancer&#39;s Recognitions&#39;&#39; and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``&nbsp; SuperHyperClique-Decompositions&#39;&#39; in the themes of jargons and buzzwords. The prefix ``SuperHyper&#39;&#39; refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions. \begin{table}[ht] \centering \caption{An Overlook On This Research And Beyond} \label{136TBLTBL} \begin{tabular}[t]{|c|c|} \hline \textcolor{black}{Advantages}&amp;\textcolor{black}{Limitations}\\ \hline \textcolor{black}{1. }\textcolor{red}{Redefining&nbsp; Neutrosophic SuperHyperGraph} &amp;\textcolor{black}{1. }\textcolor{blue}{General Results} \\&nbsp; &amp; \\ &nbsp;\textcolor{black}{2. }\textcolor{red}{&nbsp; SuperHyperClique-Decompositions}&amp; \\ &amp; \\ \textcolor{black}{3. } \textcolor{red}{Neutrosophic&nbsp;&nbsp; SuperHyperClique-Decompositions}&nbsp; &amp;\textcolor{black}{2. } \textcolor{blue}{Other SuperHyperNumbers} \\&amp; \\ \textcolor{black}{4. }\textcolor{red}{Modeling of Cancer&#39;s Recognitions}&nbsp;&nbsp;&nbsp; &amp;&nbsp; \\&amp; \\ \textcolor{black}{5. }\textcolor{red}{SuperHyperClasses}&nbsp;&nbsp;&nbsp; &amp;\textcolor{black}{3. }\textcolor{blue}{SuperHyperFamilies}&nbsp;&nbsp; \\ \hline \end{tabular} \end{table} In the Table \eqref{136TBLTBL}, benefits and avenues for this research are, figured out, pointed out and spoken out. &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperDuality} if $\forall E_i\in E&#39;,~\exists E_j\in E_{ESHG:(V,E)}\setminus E&#39;$ such that $V_a\in E_i,E_j$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperDuality} if $\forall V_i\in V&#39;,~\exists V_j\in V_{ESHG:(V,E)}\setminus V&#39;$ such that $V_i,V_j\in E_a$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperDuality).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperDuality} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperDuality; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperDuality SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperDuality, Neutrosophic re-SuperHyperDuality, Neutrosophic v-SuperHyperDuality, and Neutrosophic rv-SuperHyperDuality and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperDuality; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Extreme &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperDuality. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_5,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times1\times2)+(2\times4\times5)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2)z. \end{eqnarray*} &nbsp;&nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(2\times2\times2)z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperDuality, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}}=4z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times9+10\times6+12\times9+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperDuality SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperDuality}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperDuality SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{E_i\in E_{{P_i}^{ESHG:(V,E)}},~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward.&nbsp; Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperDuality. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality}}=\{E^{*}\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperDuality&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E^{*}_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperDuality SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E^{*}_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E^{*}_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E^{*}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}},V^{EXTERNAL}_{|E^{*}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperDuality taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E^{*}_z \equiv \\&amp;&amp; \exists! E^{*}_z\in E^{*}_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E^{*}_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperDuality. The latter is straightforward. Then there&#39;s at least one SuperHyperDuality. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperDuality could be applied. The unique embedded SuperHyperDuality proposes some longest SuperHyperDuality excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperDuality. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperJoin} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperJoin} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperJoin).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperJoin} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperJoin SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperJoin. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_2,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times5\times5 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_{13},V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 4\times5\times5z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperJoin, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}=\{E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperJoin SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperJoin. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperJoin could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperJoin. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperJoin}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperJoin SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperJoin taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperJoin. The latter is straightforward. Then there&#39;s at least one SuperHyperJoin. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperJoin could be applied. The unique embedded SuperHyperJoin proposes some longest SuperHyperJoin excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperJoin. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperPerfect} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperPerfect} if $\forall V_i\in V_{ESHG:(V,E)}\setminus V&#39;,~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperPerfect).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperPerfect} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperPerfect; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperPerfect SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperPerfect, Neutrosophic re-SuperHyperPerfect, Neutrosophic v-SuperHyperPerfect, and Neutrosophic rv-SuperHyperPerfect and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperPerfect; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperPerfect. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{{3i+24}_{i=0}^3}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}6z^8. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^7}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=6z^8. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{15},E_{16},E_{17}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}}=\{E_{{3i+1}_{i=0}^3},E_{23}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}}=3z^5. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{3i+1}_{i=0}^3},V_{15}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}=3z^5. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_3,V_6,V_8\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times4\times4z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1,E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_6,V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp; \\&amp;&amp; 3\times2z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V^{i\neq 5,7,8}_{i_{i=4}^{10}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= 5z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_3,E_9\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;3\times3 z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_1\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times5\times5)+(1\times2+1)z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{27},V_2,V_7,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; &nbsp;(1\times1\times2+1)z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_{{3i+1}_{i=0^3}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=3z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_{{2i+1}_{i=0^5}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}}= 2z^6. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=2z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperPerfect, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E_2,E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperPerfect}}=\{V_3,V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =10\times6+10\times6+12\times6+12\times6z^2. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=3z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}},{V^{EXTERNAL}}_{\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{3}}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp; \{E_i\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp; =\text{(OTHERWISE)}. \\&amp;&amp; \{\}, \\&amp;&amp; \text{If} ~\exists {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|\neq\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;= \text{(PERFECT MATCHING)}. \\&amp;&amp;=(\sum_{i=|{P}^{ESHG:(V,E)}|} (\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|)\text{choose} |{P_i}^{ESHG:(V,E)}|) \\&amp;&amp; z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp; =\text{(OTHERWISE)}0. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect}} \\&amp;&amp;=\{V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_i\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperPerfect SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperPerfect. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperPerfect could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;E_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|},V^{EXTERNAL}_{\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|+1} &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperPerfect. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect}}=\{E\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperPerfect&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperPerfect SuperHyperPolynomial}}=z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,V^{EXTERNAL}_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperPerfect taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperPerfect. The latter is straightforward. Then there&#39;s at least one SuperHyperPerfect. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperPerfect could be applied. The unique embedded SuperHyperPerfect proposes some longest SuperHyperPerfect excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperPerfect. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} \section{ Neutrosophic SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms} \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperTotal} if $\forall E_i\in E_{ESHG:(V,E)},~\exists! E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$&nbsp; and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperTotal} if $\forall V_i\in V_{ESHG:(V,E)},~\exists! V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperTotal).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperTotal} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperTotal; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperTotal SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperTotal, Neutrosophic re-SuperHyperTotal, Neutrosophic v-SuperHyperTotal, and Neutrosophic rv-SuperHyperTotal and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperTotal; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperTotal. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-}}=\{E_4,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperTotal SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_3\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= 2z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperTotal}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperTotal SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_6,E_{10}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=9z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}=\{V_1,V\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp;&nbsp; \\&amp;&amp; &nbsp; =|(|V|-1)z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}}=2z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{V_1,V_2\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}}=9z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperTotal, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperTotal}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{\frac{|E_^{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}},{V^{EXTERNAL}}_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}-1}}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperTotal SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperTotal. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperTotal could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperTotal. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal}}=\{E_i,E_j\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperTotal&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i(i-1)~|~E_i\in E^{*}_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|z^2. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal}}=\{CENTER,V_j\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperTotal SuperHyperPolynomial}}= \\&amp;&amp; (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|)~ \text{choose}~ (|V_{ESHG:(V,E)|_{\text{Neutrosophic Cardinality}}}|-1) \\&amp;&amp; z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E^{*}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperTotal taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperTotal. The latter is straightforward. Then there&#39;s at least one SuperHyperTotal. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperTotal could be applied. The unique embedded SuperHyperTotal proposes some longest SuperHyperTotal excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperTotal. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp;&nbsp;&nbsp; \section{ Neutrosophic SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V&#39;=\{V_1,V_2,\ldots,V_s\}$ and $E&#39;=\{E_1,E_2,\ldots,E_z\}.$ Then either $V&#39;$ or $E&#39;$ is called \begin{itemize} &nbsp; \item[$(i)$] \textbf{Neutrosophic e-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ and $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ \item[$(ii)$] \textbf{Neutrosophic re-SuperHyperConnected} if $\forall E_i\in E_{ESHG:(V,E)}\setminus E&#39;,~\exists E_j\in E&#39;,$ such that $V_a\in E_i,E_j;$ $\forall E_i,E_j\in E&#39;,$ such that $V_a\not\in E_i,E_j;$ and $|E_i|_{\text{NEUTROSOPIC CARDINALITY}}=|E_j|_{\text{NEUTROSOPIC CARDINALITY}};$ &nbsp;\item[$(iii)$] \textbf{Neutrosophic v-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\not\in E_a;$ and $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ \item[$(iv)$]&nbsp; \textbf{Neutrosophic rv-SuperHyperConnected} if $\forall V_i\in E_{ESHG:(V,E)}\setminus V&#39;,~\exists V_j\in V&#39;,$ such that $V_i,V_j\in E_a;$ $\forall V_i,V_j\in V&#39;,$ such that $ V_i,V_j\not\in E_a;$ and $|V_i|_{\text{NEUTROSOPIC CARDINALITY}}=|V_j|_{\text{NEUTROSOPIC CARDINALITY}};$ \item[$(v)$] \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected. \end{itemize} \end{definition} \begin{definition}((Neutrosophic) SuperHyperConnected).\\ &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$ Then $E$ is called \begin{itemize} &nbsp;\item[$(i)$] an \textbf{Extreme SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(ii)$] a \textbf{Neutrosophic SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a&nbsp; Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality&nbsp; consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(iii)$] an \textbf{Extreme SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(iv)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; \item[$(v)$] an \textbf{Extreme R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; &nbsp;\item[$(vi)$] a \textbf{Neutrosophic R-SuperHyperConnected} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; &nbsp;\item[$(vii)$] an \textbf{Extreme R-SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperConnected; and the Extreme power is corresponded to its Extreme coefficient; &nbsp;\item[$(viii)$] a \textbf{Neutrosophic SuperHyperConnected SuperHyperPolynomial} if it&#39;s either of Neutrosophic e-SuperHyperConnected, Neutrosophic re-SuperHyperConnected, Neutrosophic v-SuperHyperConnected, and Neutrosophic rv-SuperHyperConnected and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is&nbsp; the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperConnected; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. \end{itemize} \end{definition} \begin{example}\label{136EXM1} &nbsp;Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is a pair $S=(V,E)$ in the mentioned Neutrosophic Figures in every Neutrosophic items. &nbsp;\begin{itemize} &nbsp;\item On the Figure \eqref{136NSHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1$ and $E_3$ are some empty Neutrosophic &nbsp; &nbsp;SuperHyperEdges but $E_2$ is a loop Neutrosophic SuperHyperEdge and $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward.&nbsp; $E_1,E_2$ and $E_3$ are some empty Neutrosophic SuperHyperEdges but $E_4$ is a Neutrosophic SuperHyperEdge. Thus in the terms of Neutrosophic SuperHyperNeighbor, there&#39;s only one Neutrosophic SuperHyperEdge, namely, $E_4.$ The Neutrosophic SuperHyperVertex, $V_3$ is Neutrosophic isolated means that there&#39;s no Neutrosophic SuperHyperEdge has it as a Neutrosophic endpoint. Thus the Neutrosophic SuperHyperVertex, $V_3,$&nbsp; \underline{\textbf{is}} excluded in every given Neutrosophic SuperHyperConnected. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG3}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=3z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG4}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_1,E_2,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_1,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=15z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG5}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_3\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=4z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG6}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}20z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG7},&nbsp; the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_{12},E_{13},E_{14}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG8}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG9}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+1}_{i=0}^{9}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}10z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_{{i+1}_{i=11}^{19}},V_{22}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=20z^{10}. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG10}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_5\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_{12},V_{13},V_{14}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 3\times4\times4 z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG11}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_1,E_6,E_7,E_8\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=2z^4. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp;\item On the Figure \eqref{136NSHG12}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_1,E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=5z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V^{i\neq 4,5,6}_{i_{i=1}^{8}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^5. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG13}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_9,E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=3z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1,V_5\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= 3z^2. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG14}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= z. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG15}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_2,V_3,V_4\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG16}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^3. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG17}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG18}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_2,E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^3. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_1,V_2,V_6,V_{17}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= &nbsp;\\&amp;&amp; 2\times4\times3z^4. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG19}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}=\{E_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}}=11z^{10}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}}=\{V_{{i+2}_{i=0^{11}}}\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}}= 11z^{10}. \end{eqnarray*} &nbsp; \item On the Figure \eqref{136NSHG20}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected}}=\{E_6\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme SuperHyperConnected SuperHyperPolynomial}}=10z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperConnected SuperHyperPolynomial}}} &nbsp;=z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG1}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_2\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}}=z. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{V_1\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}}=10z. \end{eqnarray*} &nbsp;\item On the Figure \eqref{95NHG2}, the Neutrosophic SuperHyperNotion, namely, Neutrosophic SuperHyperConnected, is up. The Neutrosophic Algorithm is Neutrosophicly straightforward. \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected}}=\{E_3,E_4\}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Extreme Quasi-SuperHyperConnected SuperHyperPolynomial}}=z^2. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Extreme R-Quasi-SuperHyperConnected}}=\{V_3,V_{10},V_6\}. &nbsp;\\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =3\times6z^3. \end{eqnarray*} \end{itemize} \end{example} The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses. \begin{proposition} Assume a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{|{E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} be a longest path taken from a connected Neutrosophic SuperHyperPath $ESHP:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM18a} In the Figure \eqref{136NSHG18a}, the connected Neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The Neutrosophic SuperHyperSet,&nbsp; in the Neutrosophic SuperHyperModel \eqref{136NSHG18a}, is the&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then \begin{eqnarray*} &nbsp;&amp;&amp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}}= &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{E_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} &nbsp;\\&amp;&amp;=({|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1) &nbsp; \\&amp;&amp; &nbsp;z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. &nbsp;\\&amp;&amp; &nbsp;&nbsp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-Quasi-SuperHyperConnected}} &nbsp;&nbsp;&nbsp; \\&amp;&amp;=\{V^{EXTERNAL}_i\}_{i=1}^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2}. \\&amp;&amp; &nbsp; \mathcal{C}(NSHG)_{{\small\text{Neutrosophic R-Quasi-SuperHyperConnected SuperHyperPolynomial}}} &nbsp; \\&amp;&amp; =\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}} z^{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-2} \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_2,E_2, &nbsp;\\&amp;&amp;V^{EXTERNAL}_3,E_3, &nbsp;\\&amp;&amp;\ldots, &nbsp;\\&amp;&amp;{E}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1},{V^{EXTERNAL}}_{{|E_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}-1}. &nbsp;\end{eqnarray*} &nbsp;be a longest path taken from a connected Neutrosophic SuperHyperCycle $ESHC:(V,E).$ There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM19a} In the Figure \eqref{136NSHG19a}, the connected Neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, in the Neutrosophic SuperHyperModel \eqref{136NSHG19a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$ Then &nbsp; \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected&nbsp;&nbsp; SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic R-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P:V^{EXTERNAL}_i,E_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; be a longest path taken a connected Neutrosophic SuperHyperStar $ESHS:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. \end{proof} \begin{example}\label{136EXM20a} In the Figure \eqref{136NSHG20a}, the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the&nbsp; Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperStar $ESHS:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG20a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;The latter is straightforward. \end{proof} \begin{example}\label{136EXM21a} In the Neutrosophic Figure \eqref{136NSHG21a}, the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is Neutrosophic highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG21a}, is the Neutrosophic&nbsp; SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected}} \\&amp;&amp;= \{E_a\in E_{{P_i}^{ESHG:(V,E)}}, \\&amp;&amp; ~\forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}|=\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;= z^{\min|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|} \\&amp;&amp; \text{where}~ \forall {P_i}^{ESHG:(V,E)}, ~|{P_i}^{ESHG:(V,E)}| \\&amp;&amp; =\min_{i}|{P_i}^{ESHG:(V,E)}\in{P}^{ESHG:(V,E)}|\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}} \\&amp;&amp;=\{V^{EXTERNAL}_a\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},V^{EXTERNAL}_b\in V^{EXTERNAL}_{{P_i}^{ESHG:(V,E)}},~i\neq j\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=\sum_{|V^{EXTERNAL}_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}=(\sum_{i=|{P}^{ESHG:(V,E)}|} (|{P_i}^{ESHG:(V,E)}|\text{choose}~2)=z^2. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$&nbsp; There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward.&nbsp; Then there&#39;s no at least one SuperHyperConnected. Thus the notion of quasi may be up but the SuperHyperNotions based on SuperHyperConnected could be applied. There are only $z&#39;$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the &nbsp; &nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only some SuperHyperVertices and only minimum-Neutrosophic-of-SuperHyperPart SuperHyperEdges are attained in any solution &nbsp;&nbsp;&nbsp; \begin{eqnarray*} &nbsp;&amp;&amp; P: &nbsp;\\&amp;&amp; &nbsp;V^{EXTERNAL}_1,E_1, &nbsp;\\&amp;&amp;V^{EXTERNAL}_2,E_2 &nbsp;\end{eqnarray*} &nbsp;is a longest path taken from a connected&nbsp;&nbsp; Neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ The latter is straightforward. \end{proof} \begin{example}\label{136EXM22a} In the Figure \eqref{136NSHG22a}, the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and Neutrosophic featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous Neutrosophic result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG22a}, is the&nbsp; Neutrosophic SuperHyperConnected. \end{example} \begin{proposition} Assume a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then, \begin{eqnarray*} &amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected}}=\{E_i\in E^{*}_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic SuperHyperConnected SuperHyperPolynomial}} \\&amp;&amp;=|i~|~E_i\in {|{E^{*}}_{ESHG:(V,E)}|}_{\text{Neutrosophic Cardinality}}|z. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected}}=\{CENTER\in V_{ESHG:(V,E)}\}. \\&amp;&amp; \mathcal{C}(NSHG)_{\text{Neutrosophic V-SuperHyperConnected SuperHyperPolynomial}}= z. \end{eqnarray*} \end{proposition} \begin{proof} &nbsp;Let &nbsp;\begin{eqnarray*} &nbsp;&amp;&amp; P:{V^{EXTERNAL}}_i,{E^{*}}_i,CENTER,E_j. &nbsp;\end{eqnarray*} &nbsp; is a longest SuperHyperConnected taken from a connected Neutrosophic SuperHyperWheel $ESHW:(V,E).$ &nbsp;There&#39;s a new way to redefine as \begin{eqnarray*} &amp;&amp; V^{EXTERNAL}_i\sim V^{EXTERNAL}_j \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ V^{EXTERNAL}_i,V^{EXTERNAL}_j \in E_z \equiv \\&amp;&amp; \exists! E_z\in E_{ESHG:(V,E)},~ \{V^{EXTERNAL}_i,V^{EXTERNAL}_j\} \subseteq E_z. \end{eqnarray*} The term ``EXTERNAL&#39;&#39; implies $|N(V^{EXTERNAL}_i)|\geq |N(V_j)|$ where $V_j$ is corresponded to $V^{EXTERNAL}_i$ in the literatures of SuperHyperConnected. The latter is straightforward. Then there&#39;s at least one SuperHyperConnected. Thus the notion of quasi isn&#39;t up and the SuperHyperNotions based on SuperHyperConnected could be applied. The unique embedded SuperHyperConnected proposes some longest SuperHyperConnected excerpt from some representatives. The latter is straightforward. \end{proof} \begin{example}\label{136EXM23a} In the Neutrosophic Figure \eqref{136NSHG23a}, the connected Neutrosophic SuperHyperWheel $NSHW:(V,E),$ is Neutrosophic highlighted and featured. The obtained Neutrosophic SuperHyperSet, by the Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperWheel $ESHW:(V,E),$ in the Neutrosophic SuperHyperModel \eqref{136NSHG23a}, is the&nbsp; Neutrosophic SuperHyperConnected. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \end{example} &nbsp; \section{Background} There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them date back on March 09, 2023. \\ The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs&#39;&#39; in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Current Trends in Computer Science Research (JCTCSR)&rdquo; with ISO abbreviation ``J Curr Trends Comp Sci Res&#39;&#39; in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background. \\ The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&#39;&#39; in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG133} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer&rsquo;s Treatments. It&#39;s published in prestigious and fancy journal is entitled &ldquo;Journal of Mathematical Techniques and Computational Mathematics(JMTCM)&rdquo; with ISO abbreviation ``J Math Techniques Comput Math&#39;&#39; in volume 2 and issue 1 with pages 35-47. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It&#39;s the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers. \\ In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),&nbsp; ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs&#39;&#39; in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),&nbsp; ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&#39;&#39; in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),&nbsp; ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs &#39;&#39; in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39; in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&#39;&#39; in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&#39;&#39; in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&#39;&#39; in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique&#39;&#39; in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39; in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&#39;&#39; in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),&nbsp; ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39; in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39; in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)&#39;&#39;&nbsp; in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), and \cite{HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.&nbsp;&nbsp; &nbsp; \\ Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It&#39;s titled ``Beyond Neutrosophic Graphs&#39;&#39; and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. \\ Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It&#39;s titled ``Neutrosophic Duality&#39;&#39; and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It&#39;s smart to consider a set but acting on its complement that what&#39;s done in this research book which is popular in the terms of high readers in Scribd. \\ See the seminal scientific researches \cite{HG2,HG3}. The formalization of the notions on the framework of notions In SuperHyperGraphs, Neutrosophic notions In SuperHyperGraphs theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG133,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,&nbsp; on neutrosophic science is on \cite{HG39,HG40}. &nbsp; &nbsp; &nbsp; -- \begin{thebibliography}{595} \bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}&#39;&#39;, J Curr Trends Comp Sci Res 1(1) (2022) 06-14. \bibitem{HG3} Henry Garrett, &ldquo;Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes&rdquo;, J Math Techniques Comput Math 1(3) (2022) 242-263. (doi: 10.33140/JMTCM.01.03.09) \bibitem{HG133} Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf) \bibitem{HG4} Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942. https://oa.mg/work/10.5281/zenodo.6319942 \bibitem{HG5} Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}&#39;&#39; CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724. https://oa.mg/work/10.13140/rg.2.2.35241.26724 \bibitem{HG6} Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG7} Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition}&#39;&#39;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG8} Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1). \bibitem{HG9} Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}&#39;&#39;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG10} Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG11} Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG12} Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer&#39;s Circumstances Where Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG13} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG14} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG15} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, Preprints 2023, 2023010044 \bibitem{HG16} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG17}&nbsp; Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&#39;&#39;}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG18}&nbsp; Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&#39;&#39;}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG19}&nbsp; Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&#39;&#39;}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). &nbsp;\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions}&#39;&#39;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments}&#39;&#39;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}&#39;&#39;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG184} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129). \bibitem{HG183} Henry Garrett, &ldquo;New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer&#39;s Recognition With (Extreme) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009). \bibitem{HG182} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445). \bibitem{HG181} Henry Garrett, &ldquo;New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761). \bibitem{HG180} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447). \bibitem{HG179} Henry Garrett, &ldquo;New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960). \bibitem{HG178} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003). \bibitem{HG177} Henry Garrett, &ldquo;New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163). \bibitem{HG176} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401). \bibitem{HG175} Henry Garrett, &ldquo;New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720). \bibitem{HG174} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165). \bibitem{HG173} Henry Garrett, &ldquo;New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003). \bibitem{HG172} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962). \bibitem{HG171} Henry Garrett, &ldquo;New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280). \bibitem{HG170} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086). \bibitem{HG169} Henry Garrett, &ldquo;New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404). \bibitem{HG168} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). \bibitem{HG167} Henry Garrett, &ldquo;New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003). \bibitem{HG166} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641). \bibitem{HG165} Henry Garrett, &ldquo;New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967). \bibitem{HG164} Henry Garrett, &ldquo;New Ideas In Cancer&#39;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).\bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&#39;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG163} Henry Garrett, &ldquo;New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047). \bibitem{HG162} Henry Garrett, &ldquo;New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446). \bibitem{HG161} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961). \bibitem{HG160} Henry Garrett, &ldquo;New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361). \bibitem{HG159} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125). \bibitem{HG158} Henry Garrett, &ldquo;New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321). \bibitem{HG157} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441). \bibitem{HG156} Henry Garrett, &ldquo;New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer&rsquo;s Recognition With (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367). \bibitem{HG155} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048). \bibitem{HG154} Henry Garrett, &ldquo;New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286). \bibitem{HG153} &nbsp; Henry Garrett, &ldquo;New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602). \bibitem{HG152} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285). \bibitem{HG151} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569). \bibitem{HG150} Henry Garrett, &ldquo;New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer&rsquo;s Recognition with (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206). \bibitem{HG149} Henry Garrett, &ldquo;New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320). \bibitem{HG148} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161). \bibitem{HG147} Henry Garrett, &ldquo;New Ideas In Cancer&rsquo;s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241). \bibitem{HG146} Henry Garrett, &ldquo;New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243). \bibitem{HG145} Henry Garrett, &ldquo;New Ideas As Hyper Deformations On Super Chains In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806). \bibitem{HG144} Henry Garrett, &ldquo;New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123). \bibitem{HG143} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482). \bibitem{HG142} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; \bibitem{HG141} Henry Garrett, &ldquo;New Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960). \bibitem{HG140} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040). \bibitem{HG139} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125). \bibitem{HG138} Henry Garrett, &ldquo;A Research On Cancer&rsquo;s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089). \bibitem{HG137} Henry Garrett, &ldquo;New Ideas On Super Disruptions In Cancer&rsquo;s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562). \bibitem{HG136} Henry Garrett, &ldquo;Cancer&rsquo;s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968). \bibitem{HG135} &nbsp; Henry Garrett,&ldquo;Cancer&rsquo;s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525). \bibitem{HG134} Henry Garrett,&ldquo;Eulerian and Hamiltonian In Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485). \bibitem{HG133}&nbsp; Henry Garrett, &ldquo;Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, J Math Techniques Comput Math 2(1) (2023) 35-47. \bibitem{HG132} Henry Garrett,&ldquo;SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer&rsquo;s extreme Recognition&rdquo;, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1). \bibitem{HG131} Henry Garrett,&ldquo;Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer&rsquo;s neutrosophic Recognition&rdquo;, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1). \bibitem{HG130} Henry Garrett,&ldquo;The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer&rsquo;s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204). \bibitem{HG129} Henry Garrett,&ldquo;(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer&rsquo;s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925). \bibitem{HG128} Henry Garrett,&ldquo;Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer&rsquo;s Neutrosophic Recognition and Neutrosophic SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960). \bibitem{HG127} Henry Garrett,&ldquo;SuperHyperGirth Approaches on the Super Challenges on the Cancer&rsquo;s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph&rdquo;, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289). \bibitem{HG126}&nbsp; Henry Garrett,&ldquo;Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer&rsquo;s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1). \bibitem{HG125} Henry Garrett,&ldquo;Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer&rsquo;s Recognition&rdquo;, Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1). \bibitem{HG124}&nbsp; Henry Garrett,&ldquo;Neutrosophic Version Of Separates Groups Of Cells In Cancer&rsquo;s Recognition On Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).). \bibitem{HG123}&nbsp; Henry Garrett, &ldquo;The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer&rsquo;s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph&rdquo;, Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1). \bibitem{HG122} Henry Garrett,&ldquo;Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer&rsquo;s Recognition Applied in (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1). \bibitem{HG121}&nbsp; Henry Garrett, &ldquo;Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer&rsquo;s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs&rdquo;, Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1). \bibitem{HG120} Henry Garrett, &ldquo;Extremism of the Attacked Body Under the Cancer&rsquo;s Circumstances Where Cancer&rsquo;s Recognition Titled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1). \bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer&rsquo;s Recognition In Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767). \bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer&#39;s Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680). \bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer&#39;s Recognition in the Perfect Connections of Cancer&#39;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer&#39;s Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer&#39;s Recognition called Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243). \bibitem{HG116}&nbsp; Henry Garrett,&ldquo;Extreme Failed SuperHyperClique Decides the Failures on the Cancer&rsquo;s Recognition in the Perfect Connections of Cancer&rsquo;s Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs&rdquo;, ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922). \bibitem{HG115}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer&#39;s Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004). \bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer&#39;s Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849). \bibitem{HG112}&nbsp; Henry Garrett, &ldquo;Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1). \bibitem{HG111} Henry Garrett, &ldquo;Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints&rdquo;, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1). \bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer&rsquo;s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968). \bibitem{HG107} Henry Garrett, &ldquo;Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond&rdquo;, Preprints 2023, 2023010044 \bibitem{HG106} Henry Garrett, &ldquo;(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs&rdquo;, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1). \bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer&#39;s Recognition Titled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007). \bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer&rsquo;s Neutrosophic Recognitions In Special ViewPoints}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803). \bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer&rsquo;s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123). \bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer&rsquo;s Neutrosophic Recognition And Beyond}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287). \bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642). \bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer&rsquo;s Recognitions And (Neutrosophic) SuperHyperGraphs}&#39;&#39;, ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487). \bibitem{HG982}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1). \bibitem{HG98}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084). \bibitem{HG972}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1). \bibitem{HG97}&nbsp; Henry Garrett, &ldquo;(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer&rsquo;s Recognitions And Related (Neutrosophic) SuperHyperClasses&rdquo;, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923). \bibitem{HG962} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1). \bibitem{HG96} Henry Garrett, &ldquo;SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer&rsquo;s Recognitions&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640). \bibitem{HG952}&nbsp; Henry Garrett,&ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1). \bibitem{HG95} Henry Garrett, &ldquo;Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer&rsquo;s Treatments&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641). \bibitem{HG942}&nbsp; Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1). \bibitem{HG94} Henry Garrett, &ldquo;SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses&rdquo;, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966). \bibitem{HG37}&nbsp; Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph&#39;&#39;}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244). \bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}&#39;&#39;, ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160). \bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}&#39;&#39;, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf). &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}&#39;&#39;, Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf). &nbsp; \end{thebibliography} \end{document}