Vertex Equitable Labeling of Double Alternate Snake Graphs

Document Type: Research Paper

Authors

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 aA, let vf (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 labelingsuch that for all a and b in A, |vf (a) − vf (b)| ≤ 1 and the induced edge labels are 1, 2, 3, . . . , q. In this paper, we prove that DA(Tn)⊙K1DA(Tn)⊙2K1(DA(Tn) denote double alternate triangular snake) and DA(Qn) ⊙ K1DA(Qn) ⊙ 2K1(DA(Qn) denote double alternate quadrilateral snake) are vertex equitable graphs.

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