The (Integral, Mod) Sum Numbers Of Several Kinds Of Graphs

All graphs considered in this paper are finite, simple and undirected. Let N, N+ and Z denote the sets of all natural numbers , all positive integers and all integers respectively.The concept of (integral) sum graph was introduced by Harary[l,2]. LetSimilarly, we can obtain the concepts of a mod sum graph, a mod sum numbersum number and sum labelling . For convenience , throughout this paper we may assume that the vertices of G are identified with their labels.To better understand the notions of the sum graph and the integral sum graphG is the smallest number of isolated vertices which when added to G result in a (ancomplete graphs have been obtained. Among others, we have in particular the following results.In the first part of this paper, we mainly determine the (integral) sum numbers...