The distance spectral radius of digraphs

Let D(G⃗) denote the distance matrix of a strongly connected digraph G⃗. The eigenvalue of D(G⃗) with the largest modulus is called the distance spectral radius of a digraph G⃗, denoted by ϱ(G⃗). In this paper, we first give sharp upper and lower bounds for the distance spectral radius for strongly connected digraphs; we then characterize the digraphs having the maximal and minimal distance spectral radii among all strongly connected digraphs; we also determine the extremal digraph with the minimal distance spectral radius with given arc connectivity and the extremal digraph with the minimal distance spectral radius with given dichromatic number.