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## versión impresa ISSN 0716-0917

### Proyecciones (Antofagasta) vol.37 no.4 Antofagasta dic. 2018

#### http://dx.doi.org/10.4067/S0716-09172018000400613

Articles

Odd Vertex equitable even labeling of cyclic snake related graphs

1 Govindammal Aditanar College for Women Research Centre, Department of Mathematics, Tiruchendur-628215, Tamilnadu, India, e-mail : jeyajeyanthi@rediffmail.com

2 Kamaraj College of Engineering and Technology, Department of Mathematics, Virudhunagar, Tamilnadu, India, e-mail : bala_nithin@yahoo.co.in

Abstract

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 an odd vertex equitable even labeling is called an odd vertex equitable even graph. Here, we prove that the graph nC4-snake, CS(n1, n2, ..., nk), ni ≡ 0(mod4),ni ≥ 4, be a generalized kCn -snake, TÔQSn and TÕQSn are odd vertex equitable even graphs.

Keywords:  vertex equitable labeling; vertex equitable graph; odd vertex equitable even labeling; odd vertex equitable even graph.

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Received: January 2018; Accepted: March 2018

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