Bounds for the Geometric-Arithmetic index of a graph

Abstract

The first geometric-arithmetic index GA1(G), which was introduced by D. Vukičević and B. Furtula recently, is a graph-based molecular structure descriptor. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index GA1 and other well known topological indices. In particular, we relate the geometric-arithmetic index of a graph G with its first Zagreb index M1.G/, its second Zagreb index M2(G), its modified Zagreb index Z-1(G) and its Randić index R(G).