The signless Laplacian and distance signless Laplacian spectral radius of digraphs with some given parameters

Let q(G) and μ(G) denote the signless Laplacian and distance signless Laplacian spectral radius of a digraph G, respectively. In this paper, we characterize the extremal digraph which has the maximum signless Laplacian spectral radius among all strongly connected digraphs with given dichromatic number. We also determine the extremal digraph having the minimum distance signless Laplacian spectral radius among all strongly connected digraphs with given vertex connectivity.