Some results on super mean graphs

Abstract

Let G(V, E) be a graph with p vertices and q edges and f: V(G)→{1, 2, 3, ..., p + q} be an injection. For each edge e = uv, let f(e) = [f(u) + f(v)/2]. Then f is called a super mean labeling of G if f(V(G)) ∪{f(e): e ε E (G)} = {1, 2, 3, ..., p + q). A graph that admits a super mean labeling is called a super mean graph. In this paper we prove that <S_{m, n}:P_m+1>, <P_2mô K_1,n > and caterpillar are super mean graphs. We further establish that if T is a Tp-tree then T ⊙ K_n is also a super mean graph.