3-Equitable Prime Cordial Labeling of Graphs
S Murugesan, D Jayaraman and J Shiama. Article: 3-Equitable Prime Cordial Labeling of Graphs. International Journal of Applied Information Systems 5(9):1-4, July 2013. BibTeX
@article{key:article, author = "S. Murugesan and D. Jayaraman and J. Shiama", title = "Article: 3-Equitable Prime Cordial Labeling of Graphs", journal = "International Journal of Applied Information Systems", year = 2013, volume = 5, number = 9, pages = "1-4", month = "July", note = "Published by Foundation of Computer Science, New York, 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.
Reference
- F. Harary, Graph Theory, Addition-Wesley, Reading, Mass, 1972.
- David M. Burton, Elementary Number Theory, Second Edition,Wm. C. Brown Company Publishers, 1980.
- J. A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics, 17 (2010), DS6.
- L. W. Beineke and S. M. Hegde, Strongly multiplicative graphs, Discuss. Math. Graph Theory, 21(2001), 63-75.
- G. S. Bloom and S. W. Golomb, Applications of numbered undirected graphs, Proceedings of IEEE, 165(4)(1977), 562-570.
- I. Cahit, Cordial graphs, A weaker version of graceful and harmonius graphs, Ars Combinatoria, 23(1987), 201-207.
- 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.
- I. Cahit, On cordial and 3-equitable labeling of graphs, Utilitas Math, 37(1990), 189-198.
- M. Z. Youssef, A necessary condition on k-equitable labelings, Utilitas Math, 64(2003), 193-195.
- M. Sundaram, R. Ponraj and S. Somasundaram, Prime cordial labeling of graphs, Journal of Indian Academy of Mathematics, 27(2005), 373-390.
- S. K. Vaidya and P. L. Vihol , Prime cordial labeling of some graphs, Modern Applied Science, 4(8)(2010), 119-126.
Keywords
3-equitable prime cordial labeling, 3-equitable prime cordial graph