The Aα spectral radius characterization of some digraphs

Let λ(D) be the Aα spectral radius of digraph D, and let Gnr be the set of digraphs with order n and dichromatic number r. In this paper, we characterize the digraph which has the maximal Aα spectral radius in Gnr. Moreover, we also determine the unique digraph which attains the maximum (resp. minimum) Aα spectral radius among all strongly connected bicyclic digraphs.