Even vertex equitable even labeling for snake related graphs

Lourdusamy, A.; Wency, S. Jenifer; Patrick, F.; Lourdusamy, A.; Wency, S. Jenifer; Patrick, F.

doi:10.4067/S0716-09172019000100177

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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.1 Antofagasta Mar. 2019

http://dx.doi.org/10.4067/S0716-09172019000100177

Articles

Even vertex equitable even labeling for snake related graphs

A. Lourdusamy¹

S. Jenifer Wency²

F. Patrick³

^¹ St. Xavier’s College, Department of Mathematics, Palayamkottai, Tamil Nadu, India, e-mail : lourdusamy15@gmail.com

^². Reg. No. 17211282092013, St. Xavier’s College, Department of Mathematics, Palayamkottai, Manonmaniam Sundaranar University Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India, e-mail : jeniferwency@gmail.com

^³ St. Xavier’s College, Department of Mathematics, Palayamkottai, Tamil Nadu, India, e-mail : patrick881990@gmail.com

Abstract

Let G be a graph with p vertices and q edges and A = {0,2,4,···, q+1} if q is odd or A = {0,2,4,···,q} if q is even. A graph G is said to be an even 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, |v_f(a)−v_f(b)|≤1 and the induced edge labels are 2,4,···,2q, where v_f(a) be the number of vertices v with f(v)=a for a ∈ A. A graph that admits even vertex equitable even labeling is called an even vertex equitable even graph. In this paper, we prove that S(D(Q_n)), S(D(T_n)), DA(Q_m) ʘ nK₁, DA(T_m) ʘ nK₁, S(DA(Q_n)) and S(DA(T_n)) are an even vertex equitable even graphs.

Keywords: vertex equitable labeling; even vertex equitable even labeling; double quadrilateral snake; double triangular snake.

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Received: April 2018; Accepted: August 2018

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