Relevant bibliographies by topics / Prime Labeling and Prime Graphs

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Prime Labeling and Prime Graphs'

Author: Grafiati
Published: 3 June 2025
Last updated: 7 July 2025

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Journal articles on the topic "Prime Labeling and Prime Graphs"

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W., K. M. Indunil, N. Kaluarachchi K., and C. G. Perera A. "k - Odd Prime Labeling of m×n Grid Graphs." Iconic Research and Engineering Journals 6, no. 6 (2022): 7. https://doi.org/10.5281/zenodo.7439763.

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Graph labeling can be mentioned as one of the most prominent research areas in graph theory and the history of graph labeling can be traced back to the 1960s as well. There is a  quite number of graph labeling techniques such as graceful labeling, radio labeling, antimagic labeling, prime labeling, and lucky labeling. There are various subtypes of prime labeling including odd prime labeling, k- prime labeling, neighborhood prime labeling, and coprime labeling. In this study, we explore one of the prime labeling varieties called odd prime labeling. There is a well-known conjecture related to this area that all the prime graphs are odd prime graphs. There is a vast number of publications regarding prime labeling and odd prime labeling for different classes of graphs. Recent works on odd prime labeling investigate different types of snake graphs, complete graphs, triangular-type snake graphs, different types of ladder graphs, families of cycle-related and path-related graphs, etc. In this research work, we introduce the concept of k- odd prime labeling and obtain several k- odd prime graphs such as m×n grid graph and variations of it.
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Arockiamary, S. Teresa, and G. Vijayalakshmi. "Vertex k-Prime Labeling of Theta Graphs." Indian Journal Of Science And Technology 16, no. 26 (2023): 2008–15. http://dx.doi.org/10.17485/ijst/v16i26.1278.

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Mary, M. Maria Angela, and Elvina Mary L. "Prime Cordial Distance Labeling for Some Graphs." International Journal of Research Publication and Reviews 6, no. 3 (2025): 1485–91. https://doi.org/10.55248/gengpi.6.0325.1146.

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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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A., Ezhil. "TOTAL PRIME LABELING OF STAR RELATED GRAPHS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 07 (2023): 3575–77. https://doi.org/10.5281/zenodo.8175253.

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Manaloto, Korina Ernjulie, and Rovin Santos. "Prime Labeling of Some Graphs with Eisenstein Integers." SciEnggJ 16, no. 2 (2023): 329–36. http://dx.doi.org/10.54645/2023162tka-51.

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A graph on n vertices is said to admit a prime labeling if the vertices can be labeled with the first n natural numbers in such a way that two adjacent vertices have relatively prime labels. In this paper, we define an order on the set of Eisenstein integers to extend the notion of prime labeling of graphs to the set of Eisenstein integers. Properties of the ordering are studied to come up with prime labelings of some families of graphs such as the flower, wheel, centipede, and double broom graphs.
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Seoud, M. A., A. T. M. Matar, and R. A. Al-Zuraiqi. "Prime Cordial Labeling." Circulation in Computer Science 2, no. 4 (2017): 1–10. http://dx.doi.org/10.22632/ccs-2017-251-98.

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We show that some special families of graphs have prime cordial labeling. We prove that If G is not a prime cordial graph of order m then G∪K_(1,n)is a prime cordial graph if E(G)= n-1,n or n+1 , and we prove that S^' (K_(2,n)), Jelly fish graph , Jewel graph, the graph obtained by duplicating a vertex v_k in the rim of the helm H_nand the graph obtained by fusing the vertex u_1 with u_3in a Helm graphH_n are prime cordial graphs.
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S, Teresa Arockiamary, and Vijayalakshmi G. "Vertex k-Prime Labeling of Theta Graphs." Indian Journal of Science and Technology 16, no. 26 (2023): 2008–15. https://doi.org/10.17485/IJST/v16i26.1278.

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Abstract <strong>Objectives:</strong>&nbsp;To analyse some theta related graphs that admit vertex k-prime labeling for each positive integer k.&nbsp;<strong>Methods:</strong>&nbsp;In this study, vertices of the graphs are assigned with k, k+1,&hellip;,k+|V|-1 such that each pair of labels of adjacent vertices are relatively prime. Justifications for the proof are given.&nbsp;<strong>Findings:</strong>&nbsp;We examine the theta related graphs such as generalised theta graphs, uniform theta graphs, centralised uniform theta graphs for m = 1 are vertex k-prime. In addition, we introduce another structure of theta graph known as centralised generalised theta graph and show that vertex k-prime labeling exists for the graph.&nbsp;<strong>Novelty:</strong>&nbsp;Vertex k-prime labeling is a new variant of prime labeling and theta families of graphs exhibiting the labeling is a new finding. Another structure of theta graph known as centralised generalised theta graph is introduced and proved that vertex k-prime labeling exists for the graph. <strong>Keywords:</strong> Vertex k-Prime Labeling; Generalised Theta Graphs; Uniform Theta Graphs; Centralised Uniform Theta Graphs; Centralised Generalised Theta Graph
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Lakshmi., Anantha, Jayalakshmi K, and Madhavi T. "Prime Labeling of Jahangir Graphs." International Journal of Engineering & Technology 7, no. 4.10 (2018): 389. http://dx.doi.org/10.14419/ijet.v7i4.10.20944.

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The paper investigates prime labeling of Jahangir graph Jn,m for n ≥ 2, m ≥ 3 provided that nm is even. We discuss prime labeling of some graph operations viz. Fusion, Switching and Duplication to prove that the Fusion of two vertices v1 and vk where k is odd in a Jahangir graph Jn,m results to prime graph provided that the product nm is even and is relatively prime to k. The Fusion of two vertices vnm + 1 and vk for any k in Jn, m is prime. The switching of vk in the cycle Cnm of the Jahangir graph Jn,m is a prime graph provided that nm+1 is a prime number and the switching of vnm+1 in Jn, m is also a prime graph .Duplicating of vk, where k is odd integer and nm + 2 is relatively prime to k,k+2 in Jn,m is a prime graph.
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Srivastav, Dr Sweta, and Dr Sangeeta Gupta. "3-Equitable Prime Cordial Labeling of Some Graphs." International Journal of Engineering Research 4, no. 3 (2015): 115–17. http://dx.doi.org/10.17950/ijer/v4s3/306.

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Dissertations / Theses on the topic "Prime Labeling and Prime Graphs"

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Hellmuth, Marc. "Local Prime Factor Decomposition of Approximate Strong Product Graphs." Doctoral thesis, Universitätsbibliothek Leipzig, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-38755.

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In practice, graphs often occur as perturbed product structures, so-called approximate graph products. The practical application of the well-known prime factorization algorithms is therefore limited, since most graphs are prime, although they can have a product-like structure. This work is concerned with the strong graph product. Since strong product graphs G contain subgraphs that are itself products of subgraphs of the underlying factors of G, we follow the idea to develop local approaches that cover a graph by factorizable patches and then use this information to derive the global factors. First, we investigate the local structure of strong product graphs and introduce the backbone B(G) of a graph G and the so-called S1-condition. Both concepts play a central role for determining the prime factors of a strong product graph in a unique way. Then, we discuss several graph classes, in detail, NICE, CHIC and locally unrefined graphs. For each class we construct local, quasi-linear time prime factorization algorithms. Combining these results, we then derive a new local prime factorization algorithm for all graphs. Finally, we discuss approximate graph products. We use the new local factorization algorithm to derive a method for the recognition of approximate graph products. Furthermore, we evaluate the performance of this algorithm on a sample of approximate graph products.
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Sass, Catherine Bray. "Prime Character Degree Graphs of Solvable Groups having Diameter Three." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1398110266.

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Puffenberger, Owen. "Uniqueness of Bipartite Factors in Prime Factorizations Over the Direct Product of Graphs." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3017.

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While it has been known for some time that connected non-bipartite graphs have unique prime factorizations over the direct product, the same cannot be said of bipartite graphs. This is somewhat vexing, as bipartite graphs do have unique prime factorizations over other graph products (the Cartesian product, for example). However, it is fairly easy to show that a connected bipartite graph has only one prime bipartite factor, which begs the question: is such a prime bipartite factor unique? In other words, although a connected bipartite graph may have multiple prime factorizations over the direct product, do such factorizations contain the same prime bipartite factor? It has previously been shown by Hammack that when the prime bipartite factor is K_2, this is in fact true. The goal of this paper is to prove that this is in fact true for any prime bipartite factor, provided the graph being factored is R-thin. The proof of the main result takes the same initial approach as the proof by Hammack, before moving into new territory in order to prove the final result.
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Chang, Kai-Po, and 張凱博. "Prime Labellings of Trees and 4-regular Graphs." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/13484933771263747453.

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碩士<br>國立交通大學<br>應用數學系所<br>104<br>Let G be a simple and finite graph. A bijection from its vertex set onto {1,2,...,|G|} is called a prime labelling of G if any two adjacent vertices are labelling by copirme integers. Entringer conjectured that every tree has a prime labelling. In this thesis, we show that a tree T_n=(A,B) of order n>=105 with bipartition (A,B) satisfying min{|A|,|B|}<=pi(n) has a prime labelling, where pi(n) is the number of primes at most n. Moreover, we also study that the existence of a 4-regular graph with prime labelling provided the number of vertices is at least 11.
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Kuo, Jyh-Min, and 郭志銘. "On Prime Labeling Conjecture." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/91903854947271328825.

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碩士<br>國立交通大學<br>應用數學系<br>90<br>In 1980, Roger Entringer conjectured: every tree has a prime labeling. So far, this conjecture is still unsolved. As a matter of fact, only some special types of trees are verified. In this thesis, we first prove the conjecture by S. M. Lee. et al : the amalgamation of m copies of the wheel Wn that share common center, Wm,n, is prime provided that n is even. Then, in section 2.2 we show the main theorem: every tree with order n(n 16) has a modified prime labeling by using consecutive n integers. Using this theorem we are able to show that more classes of trees are prime. We believe that the idea developed in this thesis can be applied to tackle the conjecture by Roger Entringer.
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Lin, Shu-Hua, and 林淑華. "A Study of Prime Labeling." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/70942228844018801519.

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碩士<br>國立交通大學<br>應用數學系<br>87<br>Let G = (V,E) be a graph. A bijection f : V → {1,2,…,|V |} is called a prime labeling if for each e = {u,v} in E, we have gcd ( f (u) , f (v) ) = 1. A graph admits a prime labeling is called a prime graph. In 1978, Roger Entringer conjectured that every tree is a prime graph. So far, this conjecture is still unsolved. In this thesis, we study the prime labeling and we are able to show that the conjecture is true for trees of order up to 104
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BONAZZI, LORENZO. "Prime graphs of Finite Groups." Doctoral thesis, 2022. https://hdl.handle.net/2158/1294339.

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All the groups treated in the thesis are finite. Let X be a set of integers and consider the primes that divide some element of X as vertices, where two vertices are adjacent if their product divides some element of X. The graph obtained is called the prime graph on X. In this thesis we give an algebraic description of a group G in the following three cases. 1. When the Gruenberg-Kegel graph of G (that is the prime graph on the set of all group element orders) has a cut-set. 2. When the prime graph on the degrees of irreducible real characters of G has no edges. 3. When the prime graph on the lengths of real conjugacy classes has no edges. Is presented also a description of groups acting on a module in the case that the lengths of orbits are prime powers.
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Hellmuth, Marc [Verfasser]. "Local prime factor decomposition of approximate strong product graphs / vorgelegt von Marc Hellmuth." 2010. http://d-nb.info/100732130X/34.

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Books on the topic "Prime Labeling and Prime Graphs"

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Moscowitz, Leigh. Gay Marriage Goes Prime-Time. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038129.003.0004.

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This chapter examines the storytelling techniques that were used by journalists to produce the gay marriage issue for prime-time news audiences in 2003–2004, including labeling, framing, sourcing, imagery, and graphics. It discusses the discursive strategies employed by mainstream media to create conflict in the news; how sensationalist labels and descriptive language were used in news stories to validate historic homophobic discourses; and how privileging dominant political and religious sources worked to dichotomize the debate and silence moderate perspectives. It also explores how standard journalistic frames organized the same-sex marriage debate within “official” institutions of power. The chapter argues that journalistic definitions of authority, expertise, and “balance” created an uneven playing field, often pitting gay and lesbian spokespersons against unequal sources of influence from legal, medical, religious, and political authorities. It also shows how media coverage reduced the broader gay rights agenda to a single-issue movement and rarely gave gays and lesbians—almost always shown as couples—the opportunity to offer their own perspectives on this important issue.
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Book chapters on the topic "Prime Labeling and Prime Graphs"

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Parthiban, A., and N. Gnanamalar David. "On Prime Distance Labeling of Graphs." In Theoretical Computer Science and Discrete Mathematics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64419-6_31.

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Shrimali, N. P., and A. K. Rathod. "Total Neighborhood Prime Labeling of Join Graphs." In Recent Advancements in Graph Theory. CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-12.

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Teresa Arockiamary, S., and G. Vijayalakshmi. "k-Prime Total Labeling of Union of Graphs." In Springer Proceedings in Mathematics & Statistics. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-77764-6_7.

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Wu, Gang, Kuo Zhang, Can Liu, and Juanzi Li. "Adapting Prime Number Labeling Scheme for Directed Acyclic Graphs." In Database Systems for Advanced Applications. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11733836_56.

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Balamurugan, B. J., K. Thirusangu, B. J. Murali, and J. Venkateswara Rao. "Computation of Narayana Prime Cordial Labeling of Book Graphs." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01123-9_54.

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Balamurugan, B. J., K. Thirusangu, and B. J. Murali. "Computing Narayana Prime Cordial Labeling of Web Graphs and Flower Graphs." In Advances in Intelligent Systems and Computing. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-5934-7_37.

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V, Sharon Philomena, and M. Gomathi. "Edge Vertex Prime Labeling (EVPL) of Certain Trees and Graphs." In Springer Proceedings in Mathematics & Statistics. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-77764-6_17.

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Shrimali, N. P., and S. K. Singh. "Gaussian Vertex Prime Labeling of Some Graphs Obtained from Origami Models." In Recent Advancements in Graph Theory. CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-13.

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Prajapati, U. M., and A. V. Vantiya. "SD-Prime Cordial Labeling of Double k-Polygonal Snake Graph." In Recent Advancements in Graph Theory. CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-6.

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Donovan, Elizabeth A., and Lesley W. Wiglesworth. "Graph Labelings: A Prime Area to Explore." In Foundations for Undergraduate Research in Mathematics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08560-4_4.

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Conference papers on the topic "Prime Labeling and Prime Graphs"

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Kalarani, P., R. Revathi, R. Vijaykrishnaraj, A. Suganya, and K. Vijayalakshmi. "Optimized Modular Multiplicative Divisor Labeling for Efficient Minimum Spanning Tree Computation in Jellyfish Graphs Using Prims Algorithm." In 2025 8th International Conference on Trends in Electronics and Informatics (ICOEI). IEEE, 2025. https://doi.org/10.1109/icoei65986.2025.11013719.

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De Silva, K. H. C., and A. A. I. Perera. "Odd Prime Labeling of Snake Graphs." In SLIIT 2nd International Conference on Engineering and Technology. SLIIT, 2023. http://dx.doi.org/10.54389/lufm4069.

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Graph theory is one of the branches of mathematics which is concerned with the networks of points connected by lines. One of the most important research areas in graph theory is graph labeling, which dates back to the 1960s. Graph labeling is assigning integers to the vertices, edges, or both depending on conditions. Labeled graphs are helpful in mathematical models for a wide range of applications such as in coding theory, circuit theory, computer networks, and in cryptography as well. There are various types of graph labeling techniques in graph theory such as radio labeling, graceful labeling, prime labeling, antimagic labeling, and lucky labeling, etc. In this research, we use one of the variations of prime labeling called odd prime labeling of snake graphs. Recent works on odd prime labeling investigate about families of snake graphs, complete graphs, etc and there they discuss about one odd integer sequence only. In this research, we introduce odd prime labeling method for snake graphs for any odd integer sequence and we give a proof for it as well. KEYWORDS: snake graph, odd sequences, odd prime labeling, relatively prime
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Dayal, Ram, A. Parthiban, G. Samdanielthompson, and P. Selvaraju. "Prime labeling and prime distance labeling of some simple graphs." In THE FOURTH SCIENTIFIC CONFERENCE FOR ELECTRICAL ENGINEERING TECHNIQUES RESEARCH (EETR2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0170323.

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Dayal, Ram, and A. Parthiban. "Prime labeling and prime distance labeling of some classes of graphs." In INTERNATIONAL CONFERENCE ON RECENT ADVANCES IN MATHEMATICS AND COMPUTATIONAL ENGINEERING: ICRAMCE 2022. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0156720.

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Yegnanarayanan, V. "On prime distance labeling of graphs." In 2017 International Conference On Smart Technologies For Smart Nation (SmartTechCon). IEEE, 2017. http://dx.doi.org/10.1109/smarttechcon.2017.8358629.

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Meena, S., and A. Ezhil. "Total prime labeling of some subdivision graphs." In RECENT TRENDS IN PURE AND APPLIED MATHEMATICS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135219.

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Malathi, T., and K. Balasangu. "Prime labeling for some bistar related graphs." In INTERNATIONAL CONFERENCE ON RECENT TRENDS IN APPLIED MATHEMATICAL SCIENCES (ICRTAMS-2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0064375.

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Gayathri, K., A. Sasikala, and C. Sekar. "Prime cordial labeling of some special graphs." In 2ND INTERNATIONAL INTERDISCIPLINARY SCIENTIFIC CONFERENCE ON GREEN ENERGY, ENVIRONMENTAL AND RENEWABLE ENERGY, ADVANCED MATERIALS, AND SUSTAINABLE DEVELOPMENT: ICGRMSD24. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0233916.

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Annamma, V., and N. Hameeda Begum. "Prime labeling of some star related shadow graphs." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108574.

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Chandra, B., and R. Kala. "Group S3 cordial prime labeling of some splitting graphs." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2020. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0025803.

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