Document Type : Research Paper

Authors

• P. Jeyanthi ¹
• A. Maheswari ²
• M. Vijayalakshmi ³

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)⊙K₁, DA(T_n)⊙2K₁(DA(T_n) denote double alternate triangular snake) and DA(Q_n) ⊙ K₁, DA(Q_n) ⊙ 2K₁(DA(Q_n) denote double alternate quadrilateral snake) are vertex equitable graphs.

Keywords

• vertex equitable labeling
• vertex equitable graph
• double alternate triangular snake
• double alternate quadrilateral snake