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 $GA(G) =\sum_{uv\in E(G)}\frac{2\sqrt{d_u d_v}}{d_u+d_v}.$ 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.
