Some results on the distance and distance signless Laplacian spectral radius of graphs and digraphs

摘要

Let ρ(D(G)) denote the distance spectral radius of a graph G and ∂(G→) denote the distance signless Laplacian spectral radius of a digraph G→. Let Gn,kD be the set of all k-connected graphs of order n with diameter D. In this paper, we first determine the unique graph with minimum distance spectral radius in Gn,kD; we then give sharp upper and lower bounds for the distance signless Laplacian spectral radius of strongly connected digraphs; we also characterize the digraphs having the maximal and minimal distance signless Laplacian spectral radii among all strongly connected digraphs; furthermore, we determine the extremal digraph with the minimal distance signless Laplacian spectral radius with given dichromatic number.