Toughness and Aα-spectral radius in graphs

Sizhong Zhou, Yuli Zhang, Tao Zhang +1

Let $\alpha \in [0,1)$, and let $G$ be a connected graph of order $n$ with $n\ge f(\alpha )$, where $f(\alpha )=6$ for $\alpha \in [0,\frac{2}{3}]$ and $f(\alpha )=\frac{4}{1-\alpha }$ for $\alpha \in (\frac{2}{3},1)$. A gra…