^{1}1Research Center, Department of Mathematics, Govindammal Aditanar College for women, Tiruchendur - 628 215, Tamilnadu,India

^{2}2Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, India

^{3}3Department of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram, Thoothukudi District, Tamilnadu, India

Abstract

Let G be a graph with p vertices 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_{f} (b)| ≤ 1 and the induced edge labels are 1, 2, 3, . . . , q. In this paper, we prove that DA(T_{n})⊙K_{1}, DA(T_{n})⊙2K_{1}(DA(T_{n}) denote double alternate triangular snake) and DA(Q_{n}) ⊙ K_{1}, DA(Q_{n}) ⊙ 2K_{1}(DA(Q_{n}) denote double alternate quadrilateral snake) are vertex equitable graphs.