On the first geometric-arithmetic index of graphs

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of adjacent vertices. We obtain lower and upper bounds onGA1 and characterize graphs forwhich 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.