The Aα spectral radius characterization of some digraphs

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