Vertex Equitable Labeling of Cycle and Star 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, 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, |?f (?) - ?f (b)|? 1 and the induced edge labels are 1, 2, 3, , q. In this paper, we prove that jewel graph Jn, jelly fish graph (JF)n, balanced lobster graph BL(n,2,m), Ln ? Km (mean value) and <LnôK1,m> are vertex equitable graphs.