Edge mean graph

Let G = (V;E) be a finite simple undirected graph of order p and size q having no isolated vertices. Let L = f1;2; : : : ;qg except for graphs having a tree as one component in which case L0 = f0;1;2; : : : ;qg. Let f : E !L(L0) be an injection. For every v in V, let f (v) = lx d(v)m where x = å f (e), the summation being taken over all edges e incident on v and dye denotes the smallest integer greater than or equal to y. If f (v) are all distinct and belong to L(L0), we call f an edge mean labeling of G and a graph G that admits an edge mean labeling is called an edge mean graph. In other words f is an edge mean labeling of G if f induces an injection f  :V !L(L0). In this article, we investigate certain classes of graphs that admit edge mean labeling. We also show that cycles, complete graphs on 4 vertices and complete bipartite graph K2;3 are not edge mean graphs.