Vertex equitable labeling of union of cyclic snake related graphs

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 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) — vfb)| ≤ 1 and the induced edge labels are 1, 2, 3,...,q. In this paper, we prove that key graph KY(m, n), P(2.QSn), P(m.QSn), C(n.QSm), NQ(m) and K1,n X P2are vertex equitable graphs.