Sharp upper bounds on the distance spectral radius of a graph

Let M=(mij) be a nonnegative irreducible n×n matrix with diagonal entries 0. The largest eigenvalue of M is called the spectral radius of the matrix M, denoted by ρ(M). In this paper, we give two sharp upper bounds of the spectral radius of matrix M. As corollaries, we give two sharp upper bounds of the distance matrix of a graph.