New Results on the Geometric-Arithmetic Index

Abstract

Let G be a graph with vertex set VG and edge set EG. Let du denote the degree of vertex u∈VG. The geometric-arithmetic index of G is defined as GAG=∑uv∈EG2dudv/du+dv. In this paper, we obtain some new lower and upper bounds for the geometric-arithmetic index and improve some known bounds. Moreover, we investigate the relationships between geometric-arithmetic index and several other topological indices.