General Zagreb indices of composite graphs

Abstract

The first and second general Zagreb indices, M α 1 and M α 2 , are the sum of the terms δ(u) α +δ(v) α and δ(u) α •δ(v) α , respectively, over all pairs of adjacent vertices u, v of a graph, where δ(x) is the degree of the vertex x, and α is a real number.For α = 1, M α 1 and M α 2 are equal to the ordinary first and second Zagreb indices.For some other values of α, M α 1 and M α 2 reduce to a variety of other, earlier considered, topological indices.In this paper, we establish expressions for M α 1 and M α 2 for several types of composite graphs, and give examples pointing at possible applications of these expressions.