On Difference of Zagreb Indices

Abstract

The classical first and second Zagreb indices of a graph G are defined as M-1 = Sigma(v) d(v)(2) and M-2 = Sigma(uv) d(u) d(v), where d(v) is the degree of the vertex v of G. So far, the difference of M-1 and M-2 has not been studied. We show that this difference is closely related to the vertex-degree-based invariant RM2 = Sigma(uv) (d(u) - 1) (d(v) - 1), and determine a few basic properties of RM2. (C) 2014 Elsevier B.V. All rights reserved.