Sharp bounds on the spectral radius of a nonnegative matrix

We give upper and lower bounds for the spectral radius of a non-negative matrix using its row sums and characterize the equality cases if the matrix is irreducible. Then we apply these bounds to various matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, the distance matrix, the distance signless Laplacian matrix, and the reciprocal distance matrix. Some known results in the literature are generalized and improved. (C) 2013 Elsevier Inc. All rights reserved.