Mean labeling of some graphs

Abstract

Let G be a (p, q) graph and f: V (G) → {0, 1, m, 3,..., q} be an injection. For each edge e = uv, let f*(e) = [f (u)+f (v)/2]. Then f is called a mean labeling if {f*(e): e ∈ E(G)} = {1, 2, 3,..., q}. A graph that admits a mean labeling is called a mean graph. In this paper, we prove T ôCn, T õCn, T @Pn, T ©2Pn, where T is a Tp-tree, are mean graphs.