  M. Aouchiche and P. Hansen proposed the distance Laplacian and the distance
signless Laplacian of a connected graph [Two Laplacians for the distance matrix
of a graph, LAA 439 (2013) 21{33]. In this paper, we obtain three theorems on
the sharp upper bounds of the spectral radius of a nonnegative matrix, then
apply these theorems to signless Laplacian matrices and the distance signless
Laplacian matrices to obtain some sharp bounds on the spectral radius,
respectively. We also proposed a known result about the sharp bound of the
signless Laplacian spectral radius has a defect.
