Bounds for the augmented Zagreb index

Abstract

The augmented Zagreb index (AZI for short) of a graph G, introduced by Furtula et al. in 2010, is defined as AZI(G)= Σ vivj ∈ E(G)} (d(vi)d(vj)} {d(vi)+d(vj)-2)3, where E(G) is the edge set of G, and d(vi) denotes the degree of the vertex vi. In this paper, we give some new bounds on general connected graphs, molecular trees and triangle-free graphs.