Vertex Equitable Labeling of Double Alternate Snake Graphs

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 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 labeling f such 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)⊙K1,DA(Tn)⊙2K1(DA(Tn) denote double alternate triangular snake) and DA(Qn) ⊙ K1,DA(Qn) ⊙ 2K1(DA(Qn) denote double alternate quadrilateral snake) are vertex equitable graphs.