On the first geometric-arithmetic index of graphs

Abstract

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukievi, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 13691376] the first geometricarithmetic index of a graph G was defined as GA1=∑didj(di+dj)2 with summation going over all pairs of adjacent vertices. We obtain lower and upper bounds on GA1 and characterize graphs for which these bounds are best possible. Moreover, we discuss the effect on GA1 of inserting an edge into a graph. © 2011 Elsevier B.V. All rights reserved.