A sharp Randić bound for König--Egerváry graphs and a conjecture of Aouchiche, Hansen, and Zheng

Pei Liu, Feiyu Nan, Suil O +1

Let $\hat{I}{\pm }^{\prime }(G)$ be the matching number of a graph $G$, and let its Randić index be $R(G)={\sum }_{uv\in E(G)}(d(u)d(v){)}^{-1/2}$. In 2006, Aouchiche, Hansen, and Zheng conjectured that t…