Proyecciones Journal of Mathematics Vol. 35, N^o 2, pp. 177-186, June 2016. Universidad Católica del Norte Antofagasta - Chile

Vertex equitable labeling of union of cyclic snake related graphs

P. Jeyanthi

Govindammal Aditanar College for Women

A. Maheswari 

Kamaraj College of Engineering and Technology

M. Vijayalakshmi

Dr. G. U. Pope College of Engineering

India 

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ABSTRACT

Let G be a graph with p vértices and q edges and A = {0,1, 2,..., [q/2]}. A vertex labeling f : V(G) → A induces an edge labeling f * defined by f *(uv) = f (u) + f (v) for all edges uv. For a ∈ A, let v_f (a) be the number of vertices v with f (v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, |v_f(a) — v_fb)| ≤ 1 and the induced edge labels are 1, 2, 3,...,q. In this paper, we prove that key graph KY(m, n), P(2.QS_n), P(m.QS_n), C(n.QS_m), NQ(m) and K_1,n X P₂are vertex equitable graphs.

Keywords : Vertex equitable labeling, vertex equitable graph, comb graph, key graph, path union graph, quadrilateral snake graph.

AMS Subject Classification : 05C78.

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P. Jeyanthi

Research Centre Department of Mathematics Govindammal Aditanar College for Women Tiruchendur-628 215, Tamilnadu,

India

e-mail : jeyajeyanthi@rediffmail.com

A. Maheswari

Department of Mathematics

Kamaraj College of Engineering and Technology

Virudhunagar, Tamilnadu,

India

e-mail : bala_nithin@yahoo.co.in

M. Vijayalakshmi

Department of Mathematics

Dr. G. U. Pope College of Engineering

Sawyerpuram, Tamilnadu,

India

e-mail : vijLmac@rediffmail.com

   Received : May 2015. Accepted : March 2016