On the $A_{\alpha }$ spectral radius and $A_{\alpha }$ energy of non-strongly connected digraphs

Xiuwen Yang, Ligong Wang

Let $A_{\alpha }(G)$ be the $A_{\alpha }$-matrix of a digraph $G$ and ${\lambda }_{\alpha 1},{\lambda }_{\alpha 2},\dots ,{\lambda }_{\alpha n}$ be the eigenvalues of $A_{\alpha }(G)$. Let ${\rho }_{\alpha }(G)$ be the $A_{\alpha }$ spectral radius of $G$ and $E_α(G)=…