On super mean graphs

Abstract

Let G be a graph and f : V(G) -• {1,2,3,... ,p + q} be an injection. For each edge e = uv, the induced edge labeling f∗ is defined as follows: Then f is called super mean labeling if/(V(G))U{/∗(e) : E ϵ E(G)} = {1,2,3,... ,p + q}. A graph that admits a super mean labeling is called super mean graph. In this paper, we prove that the graphs Tn(g) > 1, triangular grid graph T(G), the edge mCn-snake, the braid graph B(n) and the triangular belt graph TB(α1,α2,...,αn) with α1 ≥ α2 ≥........> αn are super mean graphs. Also we prove that the graph obtained by identifying an edge of two cycles Cm and Cn is a super mean graph for m,n ≥ 3.