Survey on the general Randić index: extremal results and bounds

Abstract

For $\alpha \in ℝ$, the general Randić index of a graph $G$ is defined as $R_{\alpha }(G)={\sum }_{uv\in E(G)}{[d(u)d(v)]}^{\alpha }$, where $E(G)$ is the edge set of $G$, and $d(u)$ and $d(v)$ are the degrees of vertices $u$ and $v$ in $G$, respectively. We give a survey containing known extremal results about the general Randić index. We present results for general graphs, trees, unicyclic graphs, bicyclic graphs and chemical graphs.