On the Dα spectral radius of strongly connected digraphs

Let G be a strongly connected digraph with distance matrix D(G) and let Tr(G) the diagonal vertex transmissions of G. For any real ? [0, 1], define D?(G) as = ?Tr(G) + (1-?)D(G). The D? spectral radius is D?(G). In this paper, we first give some upper lower bounds for characterize extremal digraphs. Moreover, digraphs that are not transmission regular, bound on difference between maximum radius. Finally, obtain eigenvalues join certain regular