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Artykuły w czasopismach na temat „Double star graph”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

P, Sumathi, and Geetha Ramani G. "Arithmetic Sequential Graceful Labeling on Star Related Graphs." Indian Journal of Science and Technology 15, no. 44 (2022): 2356–62. https://doi.org/10.17485/IJST/v15i44.1863.

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Abstract <strong>Objectives:</strong> To identify a new family of Arithmetic sequential graceful graphs. <strong>Methods:</strong> The methodology involves mathematical formulation for labeling of the vertices of a given graph and subsequently establishing that these formulations give rise to arithmetic sequential graceful labeling. <strong>Findings:</strong> In this study, we analyzed some star related graphs namely Star graph, Ustar, t-star, and double star proved that these graphs possess Arithmetic sequential graceful labeling. <strong>Novelty:</strong> H

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2

Karthikeyan C. "Various Labelling for Double Star Graph." Journal of Information Systems Engineering and Management 10, no. 18s (2025): 273–77. https://doi.org/10.52783/jisem.v10i18s.2912.

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In this work, we introduce labeling techniques for the double star graph, a basic graph theory structure. In particular, we concentrate on calculating two different kinds of labeling: fortunate labeling and correct labeling. Adhering to the restrictions of vertex labeling in graph theory, appropriate labeling guarantees that neighboring vertices receive unique labels. A more recent and interesting idea is the fortunate labelling, which gives vertices positive numbers so that the labels on neighboring vertices add up to a unique value for each edge. We calculate and examine various labeling met

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3

Cao, Jingdong, Shumin Zhang, Chengfu Ye, and Tianxia Jia. "Double-Star Isolation of Maximal Outerplanar Graphs ∗." Journal of Physics: Conference Series 2660, no. 1 (2023): 012023. http://dx.doi.org/10.1088/1742-6596/2660/1/012023.

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Abstract In the graph G = (V, E), V represents the set of vertices and E represents the set of edges. ℱ represents a family of graphs. A subset S ⊆ V is considered an ℱ -isolating set if G[V\NG[S]] does not contain F as a subgraph for all F ∈ ℱ. The ℱ-isolation number of the graph G, denoted by 𝜄(G, ℱ), is defined as the minimum cardinality of an ℱ-isolating set in G. If the family ℱ consists of a single graph H, then the subset S is referred to as an H-isolating set. The H-isolation number of the graph G, denoted by 𝜄 H (G), is defined as the minimum cardinality of an H-isolating set in G. Ma

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4

Vivin.J, Vernold, Venkatachalam M., and Kaliraj K. "Harmonious coloring on double star graph families." Tamkang Journal of Mathematics 43, no. 2 (2012): 153–58. http://dx.doi.org/10.5556/j.tkjm.43.2012.675.

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In this present paper, we have proved for the line graph of double star graph, the harmonious chromatic number and the achromatic number are equal. As a motivation this work can be extended by classifying the different families of graphs for which these two numbers are equal.

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5

Venkatacha, M., N. Mohanapriy, and J. Vernold Vivin. "Star Coloring on Double Star Graph Families." Journal of Modern Mathematics and Statistics 5, no. 1 (2011): 33–36. http://dx.doi.org/10.3923/jmmstat.2011.33.36.

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6

Sugeng, K. A., Z. Z. Barack, N. Hinding, and R. Simanjuntak. "Modular Irregular Labeling on Double-Star and Friendship Graphs." Journal of Mathematics 2021 (December 28, 2021): 1–6. http://dx.doi.org/10.1155/2021/4746609.

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A modular irregular graph is a graph that admits a modular irregular labeling. A modular irregular labeling of a graph G of order n is a mapping of the set of edges of the graph to 1,2 , … , k such that the weights of all vertices are different. The vertex weight is the sum of its incident edge labels, and all vertex weights are calculated with the sum modulo n . The modular irregularity strength is the minimum largest edge label such that a modular irregular labeling can be done. In this paper, we construct a modular irregular labeling of two classes of graphs that are biregular; in this case

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7

Shirkol, Shailaja S., Pavitra P. Kumbargoudra, and Meenal M. Kaliwal. "DOUBLE ROMAN DOMINATION NUMBER OF MIDDLE GRAPH." South East Asian J. of Mathematics and Mathematical Sciences 18, no. 03 (2022): 369–80. http://dx.doi.org/10.56827/seajmms.2022.1803.31.

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For any graph G(V, E), a function f : V (G) 0, 1, 2, 3 is called Double Roman dominating function (DRDF) if the following properties holds, If f (v) = 0, then there exist two vertices v1, v2 ∈ N (v) for which f (v1) = f (v2) = 2 or there exist one vertex u ∈ N (v) for which f (u) = 3.∈ If f (v) = 1, then there exist one vertex u N (v) for which f (u) = 2 or Σ f (u) = 3. The weight of DRDF is the value w(f ) = v∈V (G) f (v). The minimum weight among all double Roman dominating function is called double Roman domination number and is denoted by γdR(G). In this article we initiated research on do

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8

P., Kavitha*1 &. A. Rajasekaran2. "PRIME LABELING IN DUPLICATE GRAPH OF SOME GRAPHS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 2 (2019): 35–45. https://doi.org/10.5281/zenodo.2558187.

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A graph with vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding such that the labels of each pair of adjacent vertices are relatively prime. A graph which admits prime labeling is called a prime graph. In this paper we prove that the duplicate graph of the path the duplicate graph of cycle the duplicate graph of star  the duplicate graph of double star  the duplicate graph of comb graph  and the duplicate graph of bistar graph for all integers  are prime labeling

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9

Senthamizh selvan J and Jahir Hussain R. "Coefficient of Range Labeling of Some Graphs." Journal of Computational Mathematica 7, no. 2 (2023): 044–56. http://dx.doi.org/10.26524/cm175.

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The coefficient of range labeling is a new type of labeling since it was introduced in 2022 by Senthamizh Selvan and Jahir Hussain. In this paper, we obtained a coefficient of range labeling for the path graph, cycle graph, sun graph, and double star graph is coefficient of range graph. We can also determine the coefficient of range value of the path graph, cycle graph, sun graph, and double star graph.

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10

Kavitha, K., and N. G. David. "Dominator Coloring on Star and Double Star Graph Families." International Journal of Computer Applications 48, no. 3 (2012): 22–25. http://dx.doi.org/10.5120/7328-0185.

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11

Aytaç, Aysun, and Ayşen Mutlu. "Double domination number of the shadow (2,3)-distance graphs." Malaya Journal of Matematik 11, no. 02 (2023): 228–38. http://dx.doi.org/10.26637/mjm1102/011.

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Let G (V,E) be a graph with the vertex set V (G) and S be a subset of V(G). If every vertex of V is dominated by S at least twice, then the set S is called a double domination set of the graph. The number of elements of the double domination set with the smallest cardinality is called double domination number and denoted by 2 (G)  notation. In this paper, we discussed the double domination parameter on some types of shadow distance graphs such as cycle, path, star, complete bipartite and wheel graphs.

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12

Kusumastuti, Nilamsari, Raventino, and Fransiskus Fran. "The diachromatic number of double star graph." Journal of Physics: Conference Series 2106, no. 1 (2021): 012024. http://dx.doi.org/10.1088/1742-6596/2106/1/012024.

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Abstract We are interested in the extension for the concept of complete colouring for oriented graph G → that has been proposed in many different notions by several authors (Edwards, Sopena, and Araujo-Pardo in 2013, 2014, and 2018, respectively). An oriented colouring is complete if for every ordered pair of colours, at least one arc in G → whose endpoints are coloured with these colours. The diachromatic number, dac ( G → ) , is the greatest number of colours in a complete oriented colouring. In this paper, we establish the formula of diachromatic numbers for double star graph, k 1 , n , n →

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13

Arundhadhi, R., and R. Sattanathan. "Acyclic Coloring on Double Star Graph Families." International Journal of Computer Applications 42, no. 18 (2012): 32–35. http://dx.doi.org/10.5120/5794-8131.

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14

R., Jahir Hussain, and Senthamizh Selvan J. "RANGE LABELING FOR SOME GRAPHS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 05 (2023): 3392–95. https://doi.org/10.5281/zenodo.7895916.

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15

Afifah, Lilla, and I. Ketut Budayasa. "PELABELAN ANGGUN GRAF BERLIAN RANGKAP BERBINTANG, BEBERAPA KELAS GRAF POHON, DAN GRAF CORONA KHUSUS." MATHunesa: Jurnal Ilmiah Matematika 11, no. 3 (2023): 368–82. http://dx.doi.org/10.26740/mathunesa.v11n3.p368-382.

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Pelabelan dari suatu graf adalah suatu pemetaan yang membawa setiap elemen graf yaitu himpunan sisi (edge) atau himpunan titik (vertex) ke bilangan bilangan bulat positif, yang disebut label. Sebuah fungsi disebut pelabelan anggun graf dengan m sisi jika adalah injektif dan fungsi terinduksi didefinisikan sebagai adalah bijektif. Graf yang mempunyai pelabelan anggun disebut graf anggun. Pada penelitian ini akan ditunjukkan konstruksi pelabelan anggun pada graf berlian rangkap berbintang , beberapa kelas graf pohon dan graf corona khusus (K_(n,n) ⨀ K_1). Kata kunci: Pelabelan anggun, graf

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16

P, Kowsalya, and Vijayalakshmi D. "On Radio k – Chromatic Number for Mycielski of Some Graphs." Indian Journal of Science and Technology 17, no. 39 (2024): 4129–37. https://doi.org/10.17485/IJST/v17i39.2315.

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Abstract <strong>Objectives:</strong> In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. <strong>Methods :</strong> This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proxim

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17

Alraqad, Tariq A., Igor Ž. Milovanović, Hicham Saber, Akbar Ali, Jaya P. Mazorodze, and Adel A. Attiya. "Minimum atom-bond sum-connectivity index of trees with a fixed order and/or number of pendent vertices." AIMS Mathematics 9, no. 2 (2024): 3707–21. http://dx.doi.org/10.3934/math.2024182.

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<abstract><p>Let $ d_u $ be the degree of a vertex $ u $ of a graph $ G $. The atom-bond sum-connectivity (ABS) index of a graph $ G $ is the sum of the numbers $ (1-2(d_v+d_w)^{-1})^{1/2} $ over all edges $ vw $ of $ G $. This paper gives the characterization of the graph possessing the minimum ABS index in the class of all trees of a fixed number of pendent vertices; the star is the unique extremal graph in the mentioned class of graphs. The problem of determining graphs possessing the minimum ABS index in the class of all trees with $ n $ vertices and $ p $ pendent vertices is a

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18

Yu, Ber-Lin, Zhongshan Li, Gu-Fang Mou, and Sanzhang Xu. "Eventual Positivity of a Class of Double Star-like Sign Patterns." Symmetry 14, no. 3 (2022): 512. http://dx.doi.org/10.3390/sym14030512.

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Identifying and classifying the potentially eventually positive sign patterns and the potentially eventually exponentially positive sign patterns of orders greater than 3 have been raised as two open problems since 2010. In this article, we investigate the potential eventual positivity of the class of double star-like sign patterns S(n,m,1) whose underlying graph G(S(n,m,1)) is obtained from the underlying graph G(S(n,m)) of the (n+m)-by-(n+m) double star sign patterns S(n,m) by adding an additional vertex adjacent to the two center vertices and removing the edge between the center vertices. W

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19

G.Nirmala, K.Anitha and S.Rajarajeswari. "Algorithm for Finding Roman Dominating Number of Extended Duplicate Graph of Star Families." February 2023 9, no. 02 (2023): 11–13. http://dx.doi.org/10.46501/ijmtst0902002.

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20

Pati, Sadashiba, Vinay Singh, and Nibedita Adhikari. "On Graph Theoretical Properties of Extended Double Star Interconnection Network Topology." Journal of Advanced Zoology 44, S-3 (2023): 1323–35. http://dx.doi.org/10.17762/jaz.v44is-3.1642.

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 The Extended Double star (EDS) parallel interconnection network with a network controller (NC) is a two-level hybrid structure. It is a large-scale network with the Double star as its basic building block. EDS network has degree (n!+n+1) and diameter ⌊(

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21

Bahadır, Selim. "Graphs with Total Domination Number Double of the Matching Number." Journal of New Theory, no. 49 (December 31, 2024): 1–6. https://doi.org/10.53570/jnt.1520557.

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A subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$. The total domination number $\gamma_t(G)$ of a graph $G$ is the minimum value of the size of a total dominating set of $G$. A subset $M$ of the edges of a graph $G$ is called a matching if no two edges of $M$ have a common vertex. The matching number $\nu (G)$ of a graph $G$ is the maximum value of the size of a matching in $G$. It can be observed that $\gamma_t(G)\leq 2\nu(G)$ holds for every graph $G$ with no isolated vertex.

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22

Kowsalya, P., and D. Vijayalakshmi. "On Radio k – Chromatic Number for Mycielski of Some Graphs." Indian Journal Of Science And Technology 17, no. 39 (2024): 4129–37. http://dx.doi.org/10.17485/ijst/v17i39.2315.

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Objectives: In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. Methods : This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proximity to one another. For a graph , with node set , edge set

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23

T. Lavanya. "Extended Reverse R Degrees of Vertices and Extended Reverse R indices of Graphs." Communications on Applied Nonlinear Analysis 31, no. 5s (2024): 110–17. http://dx.doi.org/10.52783/cana.v31.1005.

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A topological representation of a molecule is called molecular graph. A molecular graph is a collection of points representing the atoms in the molecule and set of lines represent the covalent bonds. Topological indices gather data from the graph of molecule and help to foresee properties of the concealing molecule. All the degree based topological indices have been defined through classical degree concept. In this paper, we define a novel degree concept for a vertex of a simple connected graph: Extended Reverse R degree and also, we define Extended Reverse R indices of a simple connected grap

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K.Sunitha. "Radial Radio Pell Mean Labeling of Subdivision of Graphs." Advances in Nonlinear Variational Inequalities 28, no. 2 (2024): 267–73. http://dx.doi.org/10.52783/anvi.v28.1969.

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A one-one mapping ϕ : V (G) → N for a connected graph G is defined as follows: d(x,y)+⌈(ϕ(x)+2ϕ(y))/2⌉≥1+r(G), where radius is denoted by r(G). Any vertex in G has a radial radio pell mean number of ϕ which is the maximum number and is represented by rrpmn(ϕ). Here, we look at the labeling of various graphs using the radial radio pell mean of subdivisions such as subdivision of star graph S(K_(1,n)) , subdivision of path graph S(Pn) , subdivision of friendship graph S(Fn), subdivision of wheel graph S(Wn), subdivision of quadrilateral book graph S(QB(4,3)), subdivision of closed helm graph S(C

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25

Zeen El Deen, Mohamed R., and Nora A. Omar. "Extending of Edge Even Graceful Labeling of Graphs to Strong r -Edge Even Graceful Labeling." Journal of Mathematics 2021 (April 2, 2021): 1–19. http://dx.doi.org/10.1155/2021/6643173.

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Edge even graceful labeling of a graph G with p vertices and q edges is a bijective f from the set of edge E G to the set of positive integers 2,4 , … , 2 q such that all the vertex labels f ∗ V G , given by f ∗ u = ∑ u v ∈ E G f u v mod 2 k , where k = max p , q , are pairwise distinct. There are many graphs that do not have edge even graceful labeling, so in this paper, we have extended the definition of edge even graceful labeling to r -edge even graceful labeling and strong r -edge even graceful labeling. We have obtained the necessary conditions for more path-related graphs and cycle-rela

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Kozerenko, Sergiy, and Andrii Serdiuk. "New results on imbalance graphic graphs." Opuscula Mathematica 43, no. 1 (2023): 81–100. http://dx.doi.org/10.7494/opmath.2023.43.1.81.

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An edge imbalance provides a local measure of how irregular a given graph is. In this paper, we study graphs with graphic imbalance sequences. We give a new proof of imbalance graphicness for trees and use the new idea to prove that the same holds for unicyclic graphs. We then show that antiregular graphs are imbalance graphic and consider the join operation on graphs as well as the double graph operation. Our main results are concerning imbalance graphicness of three classes of block graphs: block graphs having all cut vertices in a single block; block graphs in which the subgraph induced by

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27

Yang, Chen, and Chongmin Li. "Graph Entropy Based on Wiener Polarity Index Under Four Kinds of Graph Operations." Mathematics and Computer Science 10, no. 1 (2025): 19–25. https://doi.org/10.11648/j.mcs.20251001.13.

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The Wiener polarity index of a graph &lt;i&gt;G&lt;/i&gt;, is the number of unordered pairs of vertices that are at distance 3 in &lt;i&gt;G&lt;/i&gt;. This index can reflect the specific distance relation between vertices in the graph, and provides a new way for the study of graph structure. In this paper, the graph entropy based on Wiener polarity index defined. Based on the above definition of graph entropy, it compares the graph entropy of path and balanced double star graphs based on Wiener polarity index. The expressions of graph entropy based on Wiener po

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28

Wang, Cheng. "The effect of planetary gear/star gear on the transmission efficiency of closed differential double helical gear train." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 21 (2020): 4215–23. http://dx.doi.org/10.1177/0954406220921205.

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The research of transmission efficiency is of great significance for reducing energy consumption and improving the performance of the device. Researchers have done a lot of work on the calculation of transmission efficiency. However, in the present research work, the quantity of planetary gear/star gear is usually not considered and only a planetary gear/star gear is adopted in the gear transmission efficiency. In practice, in order to increase the stiffness and load capacity of gear train, a plurality of planetary gear/star gears is adopted. The closed differential double helical gear train h

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Das, Kinkar Chandra. "On the Exponential Atom-Bond Connectivity Index of Graphs." Mathematics 13, no. 2 (2025): 269. https://doi.org/10.3390/math13020269.

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Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: eABC=eABC(Υ)=∑vivj∈E(Υ)edi+dj−2didj, where di is the degree of the vertex vi in Υ. In this paper, we prove that the double star DSn−3,1 is the second maximal graph with respect to the eABC index of

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Vijayalakshmi, P., and K. Karuppasamy. "Analyzing Restrained Pitchfork Domination Across Path-Related Graph Structures." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 118, no. 2 (2025): 252–59. https://doi.org/10.31489/2025m2/252-259.

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Let G = (V,E) be a finite, simple, and undirected graph without an isolated vertex. A dominating subset D ⊆ V (G) is a restrained pitchfork dominating set if 1 ≤ |N(u) ∩ V − D| ≤ 2 for every u ∈ D and every vertex not in D is adjacent to at least one vertex in the same set. The cardinality of a minimum restrained pitchfork dominating set is the restrained pitchfork domination number γrpf(G). In the course of this investigation, we undertake an examination of the restrained pitchfork domination number within various path-related graphs. This analysis encompasses a range of graph structures, inc

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Lisna, P. C., and M. S. Sunitha. "b-Chromatic sum of a graph." Discrete Mathematics, Algorithms and Applications 07, no. 04 (2015): 1550040. http://dx.doi.org/10.1142/s1793830915500408.

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A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by [Formula: see text], is the maximum integer [Formula: see text] such that G admits a b-coloring with [Formula: see text] colors. In this paper we introduce a new concept, the b-chromatic sum of a graph [Formula: see text], denoted by [Formula: see text] and is defined as the minimum of sum of colors [Formula: see text] of [Formula: see text] for all [Formula: see text] i

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Rücker, Gerta, Christoph Rücker, and Ivan Gutman. "On Kites, Comets, and Stars. Sums of Eigenvector Coefficients in (Molecular) Graphs." Zeitschrift für Naturforschung A 57, no. 3-4 (2002): 143–53. http://dx.doi.org/10.1515/zna-2002-3-406.

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Two graph invariants were encountered that form the link between (molecular) walk counts and eigenvalues of graph adjacency matrices. In particular, the absolute value of the sum of coefficients of the first or principal (normalized) eigenvector, s1, and the analogous quantity sn, pertaining to the last eigenvector, appear in equations describing some limits (for infinitely long walks) of relative frequencies of several walk counts. Quantity s1 is interpreted as a measure of mixedness of a graph, and sn, which plays a role for bipartite graphs only, is interpreted as a measure of the imbalance

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Xu, Xin, Xu Zhang, and Jiawei Shao. "Planar Turán number of double star $ S_{3, 4} $." AIMS Mathematics 10, no. 1 (2025): 1628–44. https://doi.org/10.3934/math.2025075.

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<p>Planar Turán number, denoted by $ \mathrm{ex}_{\mathcal{P}}(n, H) $, is the maximum number of edges in an $ n $-vertex planar graph which does not contain $ H $ as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the topic of the planar Turán number for double stars. There were two double stars $ S_{3, 4} $ and $ S_{3, 5} $ that remained unknown. In this paper, we give the exact value of $ \mathrm{ex}_{\mathcal{P}}(n, S_{3, 4}) $.</p>

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Priyadharshini, V., and M. Nalliah. "Local distance antimagic chromatic number for the union of star and double star graphs." Ukrains’kyi Matematychnyi Zhurnal 75, no. 5 (2023): 669–82. http://dx.doi.org/10.37863/umzh.v75i5.7075.

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UDC 519.17 Let G = ( V , E ) be a graph on p vertices with no isolated vertices. A bijection f from V to { 1,2 ,3 , … , p } is called a local distance antimagic labeling if, for any two adjacent vertices u and v , we receive distinct weights (colors), where a vertex x has the weight w ( x ) = ∑ v ϵ N ( x ) f ( v ) . The local distance antimagic chromatic number χ l ⅆ a ( G ) is defined as the least number of colors used in any local distance antimagic labeling of G . We determine the local distance antimagic chromatic number for the disjoint union of t copies of stars and double stars.

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Lucci, Massimiliano, Davide Cassi, Vittorio Merlo, Roberto Russo, Gaetano Salina, and Matteo Cirillo. "Josephson Currents and Gap Enhancement in Graph Arrays of Superconductive Islands." Entropy 23, no. 7 (2021): 811. http://dx.doi.org/10.3390/e23070811.

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Evidence is reported that topological effects in graph-shaped arrays of superconducting islands can condition superconducting energy gap and transition temperature. The carriers giving rise to the new phase are couples of electrons (Cooper pairs) which, in the superconducting state, behave as predicted for bosons in our structures. The presented results have been obtained both on star and double comb-shaped arrays and the coupling between the islands is provided by Josephson junctions whose potential can be tuned by external magnetic field or temperature. Our peculiar technique for probing dis

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Shahzad, Muhammad, Muhammad Ahsan Asim, Roslan Hasni, and Ali Ahmad. "Computing Edge Irregularity Strength of Star and Banana Trees Using Algorithmic Approach." Ars Combinatoria 159, no. 1 (2024): 11–20. http://dx.doi.org/10.61091/ars159-02.

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After the Chartrand definition of graph labeling, since 1988 many graph families have been labeled through mathematical techniques. A basic approach in those labelings was to find a pattern among the labels and then prove them using sequences and series formulae. In 2018, Asim applied computer-based algorithms to overcome this limitation and label such families where mathematical solutions were either not available or the solution was not optimum. Asim et al. in 2018 introduced the algorithmic solution in the area of edge irregular labeling for computing a better upper-bound of the complete gr

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37

Septory, Brian Juned, Liliek Susilowati, Dafik Dafik, and Veerabhadraiah Lokesha. "On the Study of Rainbow Antimagic Connection Number of Comb Product of Friendship Graph and Tree." Symmetry 15, no. 1 (2022): 12. http://dx.doi.org/10.3390/sym15010012.

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Given a graph G with vertex set V(G) and edge set E(G), for the bijective function f(V(G))→{1,2,⋯,|V(G)|}, the associated weight of an edge xy∈E(G) under f is w(xy)=f(x)+f(y). If all edges have pairwise distinct weights, the function f is called an edge-antimagic vertex labeling. A path P in the vertex-labeled graph G is said to be a rainbow x−y path if for every two edges xy,x′y′∈E(P) it satisfies w(xy)≠w(x′y′). The function f is called a rainbow antimagic labeling of G if there exists a rainbow x−y path for every two vertices x,y∈V(G). We say that graph G admits a rainbow antimagic coloring

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Monikandan, S., and S. Sundar Raj. "Adversary degree associated reconstruction number of graphs." Discrete Mathematics, Algorithms and Applications 07, no. 01 (2015): 1450069. http://dx.doi.org/10.1142/s1793830914500694.

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A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card or dacard of G. The adversary degree associated reconstruction number of a graph G, adrn (G), is the minimum number k such that every collection of k dacards of G uniquely determines G. We prove that adrn (G) = 1 + min {t+1, m-t} or 1 + min {t, m - t + 2} for a graph G obtained by subdividing t edges of K1, m. We also prove that if G is a nonempty disconnected graph whose components are cycles or complete graphs, then adrn (G) is

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39

Ulaganathan, P. P., B. Selvam, and P. Vijaya kumar. "Signed Product Cordial labeling in duplicate graphs of Bistar, Double Star and Triangular Ladder Graph." International Journal of Mathematics Trends and Technology 33, no. 1 (2016): 19–24. http://dx.doi.org/10.14445/22315373/ijmtt-v33p505.

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Marsidi, Ika Hesti Agustin, Dafik, Elsa Yuli Kurniawati, and Rosanita Nisviasari. "The rainbow vertex antimagic coloring of tree graphs." Journal of Physics: Conference Series 2157, no. 1 (2022): 012019. http://dx.doi.org/10.1088/1742-6596/2157/1/012019.

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Abstract Let G(V (G),E(G)) be a connected, simple, and finite graph. Let f be a bijective function of labeling on graph G from the edge set E(G) to natural number up to the number of edges of G. A rainbow vertex antimagic labeling of graph G is a function f under the condition all internal vertices of a path u – υ, Ɐu, υ ∈ V (G) have different weight (denoted by w(u)), where w(u) = ∑ uu′∈E(G)f (uu′). If G has a rainbow vertex antimagic labeling, then G is a rainbow vertex antimagic coloring, where the every vertex is assigned with the color w(u). The rvac(G) is a notation of rainbow vertex ant

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41

Kristiana, Arika Indah, M. Hidayat, Robiatul Adawiyah, D. Dafik, Susi Setiawani, and Ridho Alfarisi. "ON LOCAL IRREGULARITY OF THE VERTEX COLORING OF THE CORONA PRODUCT OF A TREE GRAPH." Ural Mathematical Journal 8, no. 2 (2022): 94. http://dx.doi.org/10.15826/umj.2022.2.008.

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Let \(G=(V,E)\) be a graph with a vertex set \(V\) and an edge set \(E\). The graph \(G\) is said to be with a local irregular vertex coloring if there is a function \(f\) called a local irregularity vertex coloring with the properties: (i) \(l:(V(G)) \to \{ 1,2,...,k \} \) as a vertex irregular \(k\)-labeling and \(w:V(G)\to N,\) for every \(uv \in E(G),\) \({w(u)\neq w(v)}\) where \(w(u)=\sum_{v\in N(u)}l(i)\) and (ii) \(\mathrm{opt}(l)=\min\{ \max \{ l_{i}: l_{i} \ \text{is a vertex irregular labeling}\}\}\). The chromatic number of the local irregularity vertex coloring of \(G\) denoted by

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42

Lourdusamy, A., S. Kither Iammal, and I. Dhivviyanandam. "Monophonic Cover Pebbling Number \((MCPN)\) of Network Graphs." Utilitas Mathematica 121, no. 1 (2024): 11–24. https://doi.org/10.61091/um121-02.

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Given a connected graph \(G\) and a configuration \(D\) of pebbles on the vertices of \(G\), a pebbling transformation involves removing two pebbles from one vertex and placing one pebble on its adjacent vertex. A monophonic path is defined as a chordless path between two non-adjacent vertices \(u\) and \(v\). The monophonic cover pebbling number, \(\gamma_{\mu}(G)\), is the minimum number of pebbles required to ensure that, after a series of pebbling transformations using monophonic paths, all vertices of \(G\) are covered with at least one pebble each. In this paper, we determine the monopho

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43

Kristiana, Arika Indah, Sri Moeliyana Citra, Dafik, Ridho Alfarisi, and Robiatul Adawiyah. "On The Packing k-Coloring of Some Family Trees." Statistics, Optimization & Information Computing 13, no. 3 (2024): 1291–98. https://doi.org/10.19139/soic-2310-5070-2047.

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All graphs in this paper are simple and connected. Let $G=(V,E)$ be a graph where $V(G)$ is nonempty of vertex set of $G$ and $E(G)$ is possibly empty set of unordered pairs of elements of $V(G)$. The distance from $u$ to $v$ in $G$ is the length of a shortest path joining them, denoted by $d(u,v)$. For some positive integer $k$, a function $ c:V(G)\rightarrow \{1,2,...k\} $ is called packing $k-$coloring if any two not adjacent vertices $u$ and $v$, $c(u)=c(v)=i$ and $d(u,v)\geq i+1$. The minimum number $k$ such that the graph $G$ has a packing $k-$coloring is called the packing chromatic num

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44

Chartrand, Gary, and Ping Zhang. "The Ascending Ramsey Index of a Graph." Symmetry 15, no. 2 (2023): 523. http://dx.doi.org/10.3390/sym15020523.

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Let G be a graph with a given red-blue coloring c of the edges of G. An ascending Ramsey sequence in G with respect to c is a sequence G1, G2, …, Gk of pairwise edge-disjoint subgraphs of G such that each subgraph Gi (1≤i≤k) is monochromatic and Gi is isomorphic to a proper subgraph of Gi+1 (1≤i≤k−1). The ascending Ramsey index ARc(G) of G with respect to c is the maximum length of an ascending Ramsey sequence in G with respect to c. The ascending Ramsey index AR(G) of G is the minimum value of ARc(G) among all red-blue colorings c of G. It is shown that there is a connection between this conc

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45

Rajesh Kumar., T. J. "Total neighborhood prime labeling of some trees." Proyecciones (Antofagasta) 41, no. 1 (2022): 101–10. http://dx.doi.org/10.22199/issn.0717-6279-4819.

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Let G be a graph with p vertices and q edges. A total neighborhood prime labeling of G is a labeling in which the vertices and edges are assigned labels from 1 to p + q such that the gcd of labeling in the neighborhood of each non degree 1 vertex is equal to 1 and the gcd of labeling in the edges of each non degree 1 vertex is equal to 1. A graph that admits a total neighborhood prime labeling is called a total neighborhood prime graph. In this paper, we examine total neighborhood prime labeling of trees such as (n, k, m) double star trees, spiders, caterpillars and firecrackers.

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46

Xue, Jie, Ruifang Liu, and Huicai Jia. "On the distance spectrum of trees." Filomat 30, no. 6 (2016): 1559–65. http://dx.doi.org/10.2298/fil1606559x.

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Let G be a connected graph with vertex set V(G) = {v1, v2,..., vng} and edge set E(G).D(G) = (dij)nxn is the distance matrix of G, where dij denotes the distance between vi and vj. Let ?1(D) ? ?2(D)?... ? ?n(D) be the distance spectrum of G. A graph G is said to be determined by its distance spectrum if any graph having the same distance spectrum as G is isomorphic to G. Trees can not be determined by its distance spectrum. Naturally, we prove that two kinds of special trees path Pn and double star S(a,b) are determined by their distance spectra in this paper.

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Dave, Siddharth, Ryan Clark, and Regina S. K. Lee. "RSOnet: An Image-Processing Framework for a Dual-Purpose Star Tracker as an Opportunistic Space Surveillance Sensor." Sensors 22, no. 15 (2022): 5688. http://dx.doi.org/10.3390/s22155688.

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A catalogue of over 22,000 objects in Earth’s orbit is currently maintained, and that number is expected to double within the next decade. Novel data collection regimes are needed to scale our ability to detect, track, classify and characterize resident space objects in a crowded low Earth orbit. This research presents RSOnet, an image-processing framework for space domain awareness using star trackers. Star trackers are cost-effective, flight proven, and require basic image processing to be used as an attitude-determination sensor. RSOnet is designed to augment the capabilities of a star trac

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Lo Faro, Giovanni, and Antoinette Tripodi. "Bi-Squashing S2,2-Designs into (K4 − e)-Designs." Mathematics 12, no. 12 (2024): 1879. http://dx.doi.org/10.3390/math12121879.

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A double-star Sq1,q2 is the graph consisting of the union of two stars, K1,q1 and K1,q2, together with an edge joining their centers. The spectrum for Sq1,q2-designs, i.e., the set of all the n∈N such that an Sq1,q2-design of the order n exists, is well-known when q1=q2=2. In this article, S2,2-designs satisfying additional properties are investigated. We determine the spectrum for S2,2-designs that can be transformed into (K4−e)-designs by a double squash (bi-squash) passing through middle designs whose blocks are copies of a bull (the graph consisting of a triangle and two pendant edges). He

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Khabyah, Ali Al, and Moin A. Ansari. "Exploring Geometrical Properties of Annihilator Intersection Graph of Commutative Rings." Axioms 14, no. 5 (2025): 336. https://doi.org/10.3390/axioms14050336.

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Let Λ denote a commutative ring with unity and D(Λ) denote a collection of all annihilating ideals from Λ. An annihilator intersection graph of Λ is represented by the notation AIG(Λ). This graph is not directed in nature, where the vertex set is represented by D(Λ)*. There is a connection in the form of an edge between two distinct vertices ς and ϱ in AIG(Λ) iff Ann(ςϱ)≠Ann(ς)∩Ann(ϱ). In this work, we begin by categorizing commutative rings Λ, which are finite in structure, so that AIG(Λ) forms a star graph/2-outerplanar graph, and we identify the inner vertex number of AIG(Λ). In addition, a

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Zhou, Zhong. "Super-stable Kneading Sequences with Double Cycles in 1D Bimodal Maps." Journal of Computing and Electronic Information Management 11, no. 3 (2023): 42–45. http://dx.doi.org/10.54097/jceim.v11i3.10.

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It is well known that a super-stable kneading sequence (SSKS) is an important concept, all SSKSs in bimodal maps forms joints in the corresponding symbolic dynamics, it decides the multiplication table of star products, which the n-tupling bifurcations to chaos can be investigated and Feigenbaum’s metric universalities can be measured and reconstructed, this SSKSs have form which are periodic with single cycle. However, in fact, the SSKSs in bimodal maps have another form with double cycles which are little mentioned and researched, they have the same position and significance as the single cy

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