The Sigma Index of Graph Operations

Abstract

Let G be a graph of order n with vertices labeled as nu(1), nu(2),., nu(n). Let di be the degree of the vertex nu i, for i = 1, 2,., n. The sigma index, which have been defined very recently, of G is sigma(G) = Sigma(vivj epsilon E(G))(d(i) - d(j))(2). In this paper, the sigma index of the Cartesian product, composition, join and disjunction of graphs are computed. We apply some of our results to compute the sigma index of some special graph classes.