On the $A_alpha$ spectral radius and $A_alpha$ energy of non-strongly connected digraphs

Let $A_alpha(G)$ be the $A_alpha$-matrix of a digraph $G$ and $lambda_{alpha 1}, lambda_{alpha 2}, ldots, lambda_{alpha n}$ be the eigenvalues of $A_alpha(G)$. Let $rho_alpha(G)$ be the $A_alpha$ spectral radius of $G$ and $E_alpha(G)=sum_{i=1}^n lambda_{alpha i}^2$ be the $A_alpha$ energy of $G$ by using second spectral moment. Let $mathcal{G}_n^m$ be the set of non-strongly connected digraphs with order $n$, which contain a unique strong component with order $m$ and some directed trees which are hung on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal $A_alpha$ spectral radius and the maximal (minimal) $A_alpha$ energy in $mathcal{G}_n^m$.