Some new sharp bounds for the spectral radius of a nonnegative matrix and its application

Abstract

Abstract In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.

Keywords

• nonnegative matrix
• graph
• digraph
• spectral radius