CFP last date
15 April 2024
Reseach Article

3-Equitable Prime Cordial Labeling of Graphs

by S. Murugesan, D. Jayaraman, J. Shiama
International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
Volume 5 - Number 9
Year of Publication: 2013
Authors: S. Murugesan, D. Jayaraman, J. Shiama
10.5120/ijais13-450974

S. Murugesan, D. Jayaraman, J. Shiama . 3-Equitable Prime Cordial Labeling of Graphs. International Journal of Applied Information Systems. 5, 9 ( July 2013), 1-4. DOI=10.5120/ijais13-450974

@article{ 10.5120/ijais13-450974,
author = { S. Murugesan, D. Jayaraman, J. Shiama },
title = { 3-Equitable Prime Cordial Labeling of Graphs },
journal = { International Journal of Applied Information Systems },
issue_date = { July 2013 },
volume = { 5 },
number = { 9 },
month = { July },
year = { 2013 },
issn = { 2249-0868 },
pages = { 1-4 },
numpages = {9},
url = { https://www.ijais.org/archives/volume5/number9/506-0974/ },
doi = { 10.5120/ijais13-450974 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2023-07-05T17:58:57.183060+05:30
%A S. Murugesan
%A D. Jayaraman
%A J. Shiama
%T 3-Equitable Prime Cordial Labeling of Graphs
%J International Journal of Applied Information Systems
%@ 2249-0868
%V 5
%N 9
%P 1-4
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A 3-equitable prime cordial labeling of a graphGwith vertex set V is a bijection f from V to f1; 2; :::; jV jg such that if an edge uv is assigned the label 1 if gcd(f(u); f(v)) = 1 and gcd(f(u) + f(v); f(u). . f(v)) = 1, the label 2 if gcd(f(u); f(v)) = 1 and gcd(f(u) + f(v); f(u) . . f(v)) = 2 and 0 otherwise, then the number of edges labeled with i and the number of edges labeled with j differ by atmost 1 for 0 i; j 2. If a graph has a 3-equitable prime cordial labeling, then it is called a 3-equitable prime cordial graph. In this paper, we investigate the 3-equitable prime cordial labeling behaviour of paths, cycles, star graphs and complete graphs.

References
  1. F. Harary, Graph Theory, Addition-Wesley, Reading, Mass, 1972.
  2. David M. Burton, Elementary Number Theory, Second Edition,Wm. C. Brown Company Publishers, 1980.
  3. J. A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics, 17 (2010), DS6.
  4. L. W. Beineke and S. M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory, 21(2001), 63-75.
  5. G. S. Bloom and S. W. Golomb, Applications of numbered undirected graphs, Proceedings of IEEE, 165(4)(1977), 562-570.
  6. I. Cahit, Cordial graphs, A weaker version of graceful and harmonius graphs, Ars Combinatoria, 23(1987), 201-207.
  7. S. K. Vaidya, G. V. Ghodasara, Sweta Srivastav and V. J. Kaneria, Some new cordial graphs, Int. J. of Math and Math. Sci 4(2)(2008)81-92.
  8. I. Cahit, On cordial and 3-equitable labeling of graphs, Utilitas Math, 37(1990), 189-198.
  9. M. Z. Youssef, A necessary condition on k-equitable labelings, Utilitas Math, 64(2003), 193-195.
  10. M. Sundaram, R. Ponraj and S. Somasundaram, Prime cordial labeling of graphs, Journal of Indian Academy of Mathematics, 27(2005), 373-390.
  11. S. K. Vaidya and P. L. Vihol , Prime cordial labeling of some graphs, Modern Applied Science, 4(8)(2010), 119-126.
Index Terms

Computer Science
Information Sciences

Keywords

3-equitable prime cordial labeling 3-equitable prime cordial graph