# 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.

## 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

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

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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.

## Section

Artículos

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