Odd vertex equitable even labeling of graphs

Authors

  • P. Jeyanthi Govindammal Aditanar College for Women.
  • A. Maheswari Kamaraj College of Engineering and Technology.
  • M. Vijayalakshmi Dr. G. U. Pope College of Engineering.

DOI:

https://doi.org/10.4067/S0716-09172017000100001

Keywords:

Mean labeling, odd mean labeling, k-equitable labeling, vertex equitable labeling, odd vertex equitable even labeling, odd vertex equitable even graph

Abstract

In this paper, we introduce a new labeling called odd vertex equitable even labeling. Let G be a graph with p vertices and q edges and A = {1, 3,..., q} if q is odd or A = {1, 3,..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V(G) → A that induces an edge labeling f * defined by f * (uv) = f (u) + f (v) for all edges uv such that for all a and b in A, |vf (a) —vf (b)| ≤ 1 and the induced edge labels are 2, 4,..., 2q where vf (a) be the number of vertices v with f (v) = a for a ∈ A. A graph that admits odd vertex equitable even labeling is called odd vertex equitable even graph. We investigate the odd vertex equitable even behavior of some standard graphs.

Author Biographies

P. Jeyanthi, Govindammal Aditanar College for Women.

Research Centre, Department of Mathematics.

A. Maheswari, Kamaraj College of Engineering and Technology.

Department of Mathematics.

M. Vijayalakshmi, Dr. G. U. Pope College of Engineering.

Department of Mathematics.

References

[1] I. Cahit, On cordial and 3-equitable labeling of graphs, Util. Math., 37, pp. 189—198, (1990).

[2] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 17 ( 2015), #DS6.

[3] F. Harary, Graph Theory, Addison Wesley, Massachusetts, (1972).

[4] S. M. Hegde, and Sudhakar Shetty,On Graceful Trees, Applied Mathematics E- Notes, 2, pp. 192-197, (2002).

[5] A. Lourdusamy and M. Seenivasan, Vertex equitable labeling of graphs, Journal of Discrete Mathematical Sciences & Cryptography, 11(6), pp. 727—735, (2008).

[6] K. Manickam and M. Marudai, Odd mean labelings of graphs, Bulletin of Pure and Applied Sciences, 25E(1), pp. 149—153, (2006).

[7] G. Sethuraman and P. Selvaraju, Gracefulness of Arbitrary Super Subdivision of Graphs, Indian J. Pure Appl. Math., 32 (7), pp. 1059—1064, (2001).

[8] . S.Somasundaram and R. Ponraj, Mean labelings of graphs, National Academy Science letter, 26, pp. 210—213, (2003).

Published

2017-04-06

How to Cite

[1]
P. Jeyanthi, A. Maheswari, and M. Vijayalakshmi, “Odd vertex equitable even labeling of graphs”, Proyecciones (Antofagasta, On line), vol. 36, no. 1, pp. 1-11, Apr. 2017.

Issue

Section

Artículos

Similar Articles

You may also start an advanced similarity search for this article.