# Sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix

Research paper by Lihua You, Yujie Shu, Pingzhi Yuan

Indexed on: 24 Jul '15Published on: 24 Jul '15Published in: Mathematics - Combinatorics

#### Abstract

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known results about various spectral radii, including the adjacency spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance signless Laplacian spectral radius of a graph or a digraph.