ON THE A_α SPECTRAL RADIUS AND A_α ENERGY OF NON–STRONGLY CONNECTED DIGRAPHS

Let A_α (G) be the A_α-matrix of a digraph G and l_α1,l_α2,…,l_αn be the eigenvalues of A_α(G). Let ρ_α(G) be the A_α spectral radius of G and (Formula Presented) be the A_α energy of G by using second spectral moment. Let G_n^m be the set of non-strongly connected digraphs with n vertices containing a unique strong component with m vertices and some directed trees hanging on each vertex of the strong component. In this paper, we characterize the digraph which has the maximal A_α spectral radius and the maximal (or minimal) A_α energy in G_n^m.