New results on the geometric-arithmetic index (Q2666138)

Summary: Let \(G\) be a graph with vertex set \(V(G)\) and edge set \(E(G)\). Let \(d_u\) denote the degree of vertex \(u\in V(G)\). The geometric-arithmetic index of \(G\) is defined as \(\mathrm{GA}(G)=\sum_{uv \in E (G)} (2\sqrt{d_u d_v}/(d_u + d_v))\). 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.