Log in

Relevant bibliographies by topics / Prime Labeling and Prime Graphs / Journal articles

To see the other types of publications on this topic, follow the link: Prime Labeling and Prime Graphs.

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

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Prime Labeling and Prime Graphs.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

2

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

5

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

7

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

8

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.

Full text

Abstract:

Abstract <strong>Objectives:</strong> To analyse some theta related graphs that admit vertex k-prime labeling for each positive integer k. <strong>Methods:</strong> In this study, vertices of the graphs are assigned with k, k+1,…,k+|V|-1 such that each pair of labels of adjacent vertices are relatively prime. Justifications for the proof are given. <strong>Findings:</strong> 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 s

APA, Harvard, Vancouver, ISO, and other styles

9

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

10

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.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

S, Sunoj B., and Mathew Varkey T. K. "Oblong Mean Prime Labeling of Some Tree Graphs." International Journal of Trend in Scientific Research and Development Volume-2, Issue-2 (2018): 222–26. http://dx.doi.org/10.31142/ijtsrd8375.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

V., Ganesan, Mahalakshmi S., and P. Sathya M. "PRIME LABELING OF TRIANGULAR BOOK AND CYCLE-CACTUS GRAPHS." International Journal of Scientific Research and Modern Education 2, no. 2 (2017): 16–20. https://doi.org/10.5281/zenodo.848315.

Full text

Abstract:

In this paper, we prove that the Triangular book and Cycle-Cactus graphs are prime graphs. Here, we investigate and prove that new results for Triangular book admits prime labeling when is even and odd separately. We also show that the Cycle-Cactus <sup> </sup>admits prime labeling for all and where .

APA, Harvard, Vancouver, ISO, and other styles

13

Bigham, Abigail, Elizabeth Ann Donovan, James Pack, Jordan Turley, and Lesley Wiglesworth. "Prime Labelings of Snake Graphs." PUMP Journal of Undergraduate Research 2 (August 21, 2019): 131–49. http://dx.doi.org/10.46787/pump.v2i0.1274.

Full text

Abstract:

A prime labeling of a graph G with n vertices is a labeling of the vertices with distinct integers from the set {1, 2 ,..., n} such that the labels of any two adjacent vertices are relatively prime. In this paper, we introduce a snake graph, the fused union of identical cycles, and define a consecutive snake prime labeling for this new family of graphs. We characterize some snake graphs that have a consecutive snake prime labeling and then consider a variation of this labeling.

APA, Harvard, Vancouver, ISO, and other styles

14

Sunoj, B. S*1 &. Mathew Varkey T. K. 2. "LINEAR PRIME LABELING OF SOME DIRECT TREE GRAPHS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 7 (2018): 154–60. https://doi.org/10.5281/zenodo.1307142.

Full text

Abstract:

Linear prime labeling of a graph is the labeling of the vertices with {0,1,2---,p-1} and the direct edges with twice the value of the terminal vertex plus value of the initial vertex. The greatest common incidence number of a vertex (gcin) of in degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of in degree greater than one is one, then the graph admits linear prime labeling. Here we investigate some direct tree graphs for linear prime labeling.

APA, Harvard, Vancouver, ISO, and other styles

15

Youssef, Maged Zakaria, and Zainab Saad Almoreed. "On odd prime labeling of graphs." Open Journal of Discrete Applied Mathematics 3, no. 3 (2020): 33–40. http://dx.doi.org/10.30538/psrp-odam2020.0041.

Full text

Abstract:

In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, ...,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an <i>odd prime graph</i>. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph

APA, Harvard, Vancouver, ISO, and other styles

16

Dr., A. Ezhil. "PRIME LABELLING FOR SOME BIPARTIATE RELATED GRAPHS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 07 (2023): 3571–74. https://doi.org/10.5281/zenodo.8175239.

Full text

Abstract:

A graph G = (V,E) with ‘n’ vertices is said to have a prime labeling if its vertices are labelled with distinct positive integers not exceeding n such that for each pair of adjacent vertices are relatively prime.  A graph G which admits prime labeling is called a prime graph.  In this paper, we investigate prime labeling for some bipartiate and cycle related graphs.  We also discuss the prime labeling of some graph operation namely joint sum and path joining of bipartiate and cycle graphs

APA, Harvard, Vancouver, ISO, and other styles

17

Sunoj, B. S., and Varkey T. K. Mathew. "Oblong Mean Prime Labeling of Some Tree Graphs." International Journal of Trend in Scientific Research and Development 2, no. 2 (2018): 222–26. https://doi.org/10.31142/ijtsrd8375.

Full text

Abstract:

The labeling of a graph, we mean assign some integers to the vertices or edges or both of the graph. Here the vertices of the graph are labeled with oblong numbers and the edges are labeled with mean of the end vertex labels. Here the greatest common incidence number gcin of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits oblong mean prime labeling. Here we characterize some tree graphs for oblong mean prime labeling. Sunoj B S | Mathew Varkey T K

APA, Harvard, Vancouver, ISO, and other styles

18

V., Ganesan, and K. Balamurugan Dr. "PRIME LABELING FOR SOME SUNLET RELATED GRAPHS." International Journal of Scientific Research and Modern Education 1, no. 2 (2016): 1–10. https://doi.org/10.5281/zenodo.62009.

Full text

Abstract:

<em>A graph </em> <em> with vertex set </em> <em> is said to have a prime labeling if its vertices are labeled with distinct integers </em> <em> such that for each </em> <em> the labels assigned to </em> <em> and </em> <em> are relatively prime.A graph which admits prime labeling is called a prime graph. In this paper, we investigate prime labeling for some sunlet related graphs. We also discuss prime labeling in the context of some graph operations namely fusion, duplication, switching and path union.</em>

APA, Harvard, Vancouver, ISO, and other styles

19

Weerarathna, M. D. M. C. P., T. R. D. S. M. Thennakoon, K. D. E. Dhananjaya, and A. A. I. Perera. "Prime labeling of special graphs." Journal of Science 12, no. 1 (2021): 1. http://dx.doi.org/10.4038/jsc.v12i1.30.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Jesintha, J. Jeba, N. K. Vinodhini, and K. S. D. Subiksha. "Prime labeling of certain graphs*." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 40e, no. 2 (2021): 167–71. http://dx.doi.org/10.5958/2320-3226.2021.00019.9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Samuel, A. Edward, and S. Kalaivani. "Prime Labeling to Drums Graphs." Annals of Pure and Applied Mathematics 16, no. 2 (2018): 307–12. http://dx.doi.org/10.22457/apam.v16n2a7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Samuel, A. Edward, and S. Kalai vani. "Prime Labeling to Brush Graphs." International Journal of Mathematics Trends and Technology 55, no. 4 (2018): 259–62. http://dx.doi.org/10.14445/22315373/ijmtt-v55p533.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

M. Ganeshan. "Results on Prime labeling and square difference labeling of Graphs." Tuijin Jishu/Journal of Propulsion Technology 44, no. 5 (2023): 560–67. http://dx.doi.org/10.52783/tjjpt.v44.i5.2517.

Full text

Abstract:

The insight of labeling to the vertices and edges in graphs has flourished with types of labeling being applied in different areas by the researchers. Prominent among the types of labeling is Prime labeling and square difference labeling, of graphs. In this paper we show the admittance of Prime labeling and square difference labeling for few finite, simple, connected and undirected graphs.

APA, Harvard, Vancouver, ISO, and other styles

24

Bapat, Mukund. "WHEEL RELATED ONE POINT UNION OF VERTEX PRIME GRAPHS AND INVARIANCE." International Journal of Engineering Technologies and Management Research 5, no. 3 (2020): 145–50. http://dx.doi.org/10.29121/ijetmr.v5.i3.2018.186.

Full text

Abstract:

We investigate one point unions of W4, and graphs obtained from W4 such as gear graph G4, each cycle edge of W4 replaced with Pm, each pokes of W4 replaced with Pm for vertex prime labeling. All different non isomorphic structures of these graphs obtained by taking one point union graphs are shown to be vertex prime. This property of graphs is called as invariance under vertex prime labeling.

APA, Harvard, Vancouver, ISO, and other styles

25

Pappa, Dr S. Alice, and G. J. Jeba Selvi Kavitha. "Square Difference Prime Labeling for Duplication of Graphs." International Journal of Engineering and Advanced Technology 12, no. 2 (2022): 19–21. http://dx.doi.org/10.35940/ijeat.b3867.1212222.

Full text

Abstract:

Let G(V, E) be a graph with pvertices and qedges. Let f∶ V (G) → {0,1,2,…, p-1} be a bijection such that the induced function f*: E(G) → N defined by f_sqdp* (uv)=|[f(u) ]2-[f(v) ]2 | for everyuv∈E(G).If f_sqdp* is injective, then f_sqdp*is calledsquare difference labeling of G.A graph Gwhich admits square difference labeling is called square difference graph. The greatest common incidence number (gcin) of a vertex v of degree v > 1 is defined as the greatest common divisor (g.c.d) of the labels of the incident edges on v. A square difference labeling fis said to be a square difference prim

APA, Harvard, Vancouver, ISO, and other styles

26

Mukund, V. Bapat. "WHEEL RELATED ONE POINT UNION OF VERTEX PRIME GRAPHS AND INVARIANCE." International Journal of Engineering Technologies and Management Research 5, no. 3 (2018): 145–50. https://doi.org/10.5281/zenodo.1216849.

Full text

Abstract:

<strong><em>We investigate one point unions of W4, and graphs obtained from W4 such as gear graph G4, each cycle edge of W4 replaced with Pm, each pokes of W4 replaced with Pm for vertex prime labeling. All different non isomorphic structures of these graphs obtained by taking one point union graphs are shown to be vertex prime. This property of graphs is called as invariance under vertex prime labeling</em>.</strong>

APA, Harvard, Vancouver, ISO, and other styles

27

Janani R. "On Edge Prime Index of a Graph." Communications on Applied Nonlinear Analysis 31, no. 2 (2024): 42–54. http://dx.doi.org/10.52783/cana.v31.512.

Full text

Abstract:

Relatively Prime Edge labeling extends the notion of prime labeling by considering edges. Prime labeling requires adjacent vertices to possess relatively prime labels, while relatively prime edge labeling requires adjacent edges to have relatively prime labels. The transformation of a coprime edge-labeled graph into a relatively prime edge-labeled graph introduces the concept of Edge Prime Index (or Relatively Prime Index). This study focuses on cases where a coprime edge-labeled graph can be converted into a relatively prime edge-labeled graph by removing certain edges from graph G, thereby e

APA, Harvard, Vancouver, ISO, and other styles

28

Dr., S. Alice Pappa, and Jeba Selvi Kavitha G.J. "Square Difference Prime Labeling for Duplication of Graphs." International Journal of Engineering and Advanced Technology (IJEAT) 12, no. 2 (2022): 19–21. https://doi.org/10.35940/ijeat.B3867.1212222.

Full text

Abstract:

<strong>Abstract: </strong>Let 𝑮(𝑽,𝑬) be a graph with 𝒑 vertices and 𝒒 edges. Let 𝒇∶ 𝑽 (𝑮) → {𝟎,𝟏,𝟐,...,𝒑−𝟏} be a bijection such that the induced function 𝒇&lowast;∶ 𝑬(𝑮) → 𝑵 defined by 𝒇𝒔𝒒𝒅𝒑&lowast;(𝒖𝒗)=|[𝒇(𝒖)]𝟐−[𝒇(𝒗)]𝟐| for every𝒖𝒗∈𝑬(𝑮).If 𝒇𝒔𝒒𝒅𝒑&lowast; is injective, then 𝒇𝒔𝒒𝒅𝒑&lowast; is called square difference labeling of 𝑮. A graph 𝑮 which admits square difference labeling is called square difference graph. The greatest common incidence number (gcin) of a vertex v of degree 𝒗 > 𝟏 is defined as the greatest common divisor (g.c.d) of the labels of the incident

APA, Harvard, Vancouver, ISO, and other styles

29

G. Megala and K. Annadurai. "k-TRIANGULAR PRIME CORDIAL LABELING OF MAXIMAL OUTERPLANAR GRAPHS." jnanabha 52, no. 02 (2022): 126–37. http://dx.doi.org/10.58250/jnanabha.2022.52215.

Full text

Abstract:

In this paper, we study graph labeling, namely, k- triangular prime cordial labeling for k = 1, 2, 3, 4, 5, 6. This is a simple extension of prime cordial labeling where the vertex labels are defined as the higher order triangular numbers. Also we show that the maximal outerplanar graphs are k- triangular prime cordial under certain conditio

APA, Harvard, Vancouver, ISO, and other styles

30

A. Delman, S. Koilraj, and P. Lawrence Rozario Raj. "SD and k-SD Prime Cordial graphs." International Journal of Fuzzy Mathematical Archive 15, no. 02 (2018): 189–95. http://dx.doi.org/10.22457/ijfma.v15n2a9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

AbuGhneim, Omar A., and Baha' Abughazaleh. "Prime Labeling of Union of Some Graphs." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3557–66. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5336.

Full text

Abstract:

A prime labeling of a graph G is a map from the vertex set of G to the set {1, 2, ..., |V (G)|} such that any two adjacent vertices in the graph G have labels that are relatively prime. In this paper, we discuss when the disjoint union of some graphs is a prime graph.

APA, Harvard, Vancouver, ISO, and other styles

32

K, Periasamy, Venugopal K, and Lawrence Rozario Raj P. "Kth Fibonacci Prime Labeling of Graphs." International Journal of Mathematics Trends and Technology 68, no. 5 (2022): 61–67. http://dx.doi.org/10.14445/22315373/ijmtt-v68i5p510.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Gayathri, K., A. Sasikala, and C. Sekar. "Prime Cordial Labeling of Some Graphs." Journal of Physics: Conference Series 1947, no. 1 (2021): 012016. http://dx.doi.org/10.1088/1742-6596/1947/1/012016.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Vaidya, Samir K., and Nirav H. Shah. "Prime Cordial Labeling of Some Graphs." Open Journal of Discrete Mathematics 02, no. 01 (2012): 11–16. http://dx.doi.org/10.4236/ojdm.2012.21003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

S. Meena, and A. Ezhil. "Total Prime Labeling of Some Graphs." International Journal of Research in Advent Technology 7, no. 1 (2019): 115–23. http://dx.doi.org/10.32622/ijrat.71201941.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Deng, Fei, and Xing-Sheng Du. "On the Prime Labeling of Graphs." Journal of Computational and Theoretical Nanoscience 11, no. 7 (2014): 1656–59. http://dx.doi.org/10.1166/jctn.2014.3547.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Shrimali, N. P., A. K. Rathod, and P. L. Vihol. "Neighborhood-Prime labeling for some graphs." Malaya Journal of Matematik 7, no. 1 (2019): 108–12. http://dx.doi.org/10.26637/mjm0701/0021.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Simaringa, M., and S. Muthukumaran. "Edge vertex prime labeling of graphs." Malaya Journal of Matematik 7, no. 3 (2019): 572–78. http://dx.doi.org/10.26637/mjm0703/0034.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Aljouiee, Abdullah. "On Prime Cordial Labeling of Graphs." Kyungpook mathematical journal 56, no. 1 (2016): 41–46. http://dx.doi.org/10.5666/kmj.2016.56.1.41.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Arockiamary, S. Teresa, J. Baskar Babujee, and G. Vijayalakshmi Vijayalakshmi. "k-PRIME TOTAL LABELING OF GRAPHS." Advances and Applications in Discrete Mathematics 35 (November 15, 2022): 45–59. http://dx.doi.org/10.17654/0974165822051.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Ranasinghe, P. G. R. S., and L. R. M. K. R. Jayathilaka. "On Prime Labeling of Snake Graphs." Journal of Advances in Mathematics and Computer Science 38, no. 9 (2023): 135–43. http://dx.doi.org/10.9734/jamcs/2023/v38i91811.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

V., Ganesan, and K. Balamurugan Dr. "ON PRIME LABELING OF CUBIC GRAPH WITH 8 VERTICES." International Journal of Multidisciplinary Research and Modern Education (IJMRME) 2, no. 2 (2016): 49–54. https://doi.org/10.5281/zenodo.61806.

Full text

Abstract:

<em>In this paper, we show that the cubic graph on 8 vertices admits prime labeling, we also proved that the graphs obtained by merging (or) fusion of two vertices, duplication of an arbitrary vertex and switching of an arbitrary vertex in the cubic graph are prime graphs.</em>

APA, Harvard, Vancouver, ISO, and other styles

43

Parthiban, A., Ajaz Ahmad Pir, and A. Felix. "Certain Results on Prime and Prime Distance Labeling of Graphs." Journal of Physics: Conference Series 1531 (May 2020): 012062. http://dx.doi.org/10.1088/1742-6596/1531/1/012062.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Sunoj, B. S., and Mathew T. K. Varkey. "Hexagonal Difference Prime Labeling of Some Path Graphs." Mapana - Journal of Sciences 16, no. 3 (2017): 41–46. http://dx.doi.org/10.12723/mjs.42.4.

Full text

Abstract:

Hexagonal difference prime labeling of vertices of a graph is the labeling of the vertices of the graph with hexagonal numbers and the edges with absolute value of the difference of the labels of the incident vertices. The greatest common incidence number (gcin) of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits hexagonal difference prime labeling. Here we identify some path related graphs for hexagonal difference prime labeling.

APA, Harvard, Vancouver, ISO, and other styles

45

S. K. Vaidya and N. H. Shah. "Prime cordial labeling of some wheel related graphs." Malaya Journal of Matematik 1, no. 04 (2013): 148–56. http://dx.doi.org/10.26637/mjm104/017.

Full text

Abstract:

A prime cordial labeling of a graph $G$ with the vertex set $V(G)$ is a bijection $f: V(G) \rightarrow\{1,2,3, \ldots,|V(G)|\}$ such that each edge $u v$ is assigned the label 1 if $\operatorname{gcd}(f(u), f(v))=1$ and 0 if $\operatorname{gcd}(f(u), f(v))>1$, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1 . A graph which admits prime cordial labeling is called prime cordial graph. In this paper we prove that the gear graph $G_n$ admits prime cordial labeling for $n \geq 4$. We also show that the helm $H_n$ for every $n$, the closed helm $

APA, Harvard, Vancouver, ISO, and other styles

46

Ponraj, R., and J. Maruthamani. "\(4\)-Total Prime Cordial Labeling of Some Derived Graphs." Ars Combinatoria 159, no. 1 (2024): 31–40. http://dx.doi.org/10.61091/ars159-04.

Full text

Abstract:

Let \(G\) be a \((p, q)\) graph. Let \(f: V(G) \to \{1, 2, \ldots, k\}\) be a map where \(k \in \mathbb{N}\) is a variable and \(k > 1\). For each edge \(uv\), assign the label \(\gcd(f(u), f(v))\). \(f\) is called \(k\)-Total prime cordial labeling of \(G\) if \(\left|t_{f}(i) – t_{f}(j)\right| \leq 1\), \(i, j \in \{1, 2, \ldots, k\}\) where \(t_{f}(x)\) denotes the total number of vertices and edges labeled with \(x\). A graph with a \(k\)-total prime cordial labeling is called \(k\)-total prime cordial graph. In this paper, we investigate the 4-total prime cordial labeling of some graph

APA, Harvard, Vancouver, ISO, and other styles

47

Barnabas, George, and V. Yegnanarayanan. "Chromatic coloring of distance graphs, III." Proyecciones (Antofagasta) 42, no. 1 (2023): 175–204. http://dx.doi.org/10.22199/issn.0717-6279-5689.

Full text

Abstract:

A graph G(Z, D) with vertex set Z is called an integer distance graph if its edge set is obtained by joining two elements of Z by an edge whenever their absolute difference is a member of D. When D = P or D ⊆ P where P is the set of all prime numbers then we call it a prime distance graph. After establishing the chromatic number of G(Z, P ) as four, Eggleton has classified the collection of graphs as belonging to class i if the chromatic number of G(Z, D) is i. The problem of characterizing the family of graphs belonging to class i when D is of any given size is open for the past few decades.

APA, Harvard, Vancouver, ISO, and other styles

48

Pardo-Guerra, Sebastian, Vivek Kurien George, Vikash Morar, Joshua Roldan, and Gabriel Alex Silva. "Extending Undirected Graph Techniques to Directed Graphs via Category Theory." Mathematics 12, no. 9 (2024): 1357. http://dx.doi.org/10.3390/math12091357.

Full text

Abstract:

We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘prime graphs category’; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs

APA, Harvard, Vancouver, ISO, and other styles

49

Yamini M Parmar. "Edge Vertex Prime Labeling for K2,n and K3,n Graphs." Mathematical Journal of Interdisciplinary Sciences 6, no. 2 (2018): 167–80. http://dx.doi.org/10.15415/mjis.2018.62012.

Full text

Abstract:

In my study, I inspect edge vertex prime labeling of some graphs like complete bipartite graphs K2,n & K 3,n . I proved that the graphs K 2,n for every n & K 3,n for n = 3, 4, …, 29 are edge vertex prime.

APA, Harvard, Vancouver, ISO, and other styles

50

Bharat Suthar. "A Study on Odd Prime Labeling of Octopus Graphs Families." Journal of Information Systems Engineering and Management 10, no. 23s (2025): 748–53. https://doi.org/10.52783/jisem.v10i23s.3775.

Full text

Abstract:

An odd prime labeling of a graph G (V,E), is defined as a bijective function f mapping the vertex set V to the set {1,3,5,…,2|V(G)|1}, such that for every edge uvE. the greatest common divisor gcd(f(u),f(v))=1. A graph that permits such a labeling is referred to as an odd prime graph. In this study, we explore the odd prime labeling properties of various graph structures, including the octopus chain graph, octopus ladder graph, twisted octopus ladder graph, and hexa-octopus chain graph.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!