Zagreb indices of graphs with added edges

Abstract

Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar graphs. In this paper, as a sequel to a recent paper on edge deletion, we consider the change in the first and second Zagreb indices of a simple graph G when an arbitrary edge is added. This can be used to calculate the first and second Zagreb indices of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite and tadpole graphs are given.