LAUSR

Let $G$ be a graph with vertex set $V\left(G\right)$ and edge set $E\left(G\right)$ . Let $d_u$ denote the degree of vertex $u\in V\left(G\right)$ . The geometric-arithmetic index of $G$ is defined as $\text{GA}\left(G\right)={\displaystyle {\sum }_{uv\in E\left(G\right)}\left(2\sqrt{d_u{d}_v}/\left(d_u+d_v\right)\right)}$ . 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.