New Results on the Geometric-Arithmetic Index

Let G be a graph with vertex set V G and edge set E G . Let d u denote the degree of vertex u ∈ V G . The geometric-arithmetic index of G is defined as GA G = ∑ u v ∈ E G 2 d u d v / d u + d v . 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.