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

TL;DR

This paper derives precise upper and lower bounds for the spectral radius of nonnegative irreducible matrices and applies these bounds to various graph-related matrices, improving understanding of their spectral properties.

Contribution

It provides new sharp bounds for the spectral radius of nonnegative irreducible matrices and extends these results to several graph-associated matrices, yielding new and known spectral radius inequalities.

Findings

Established sharp bounds for spectral radius of nonnegative irreducible matrices.

Applied bounds to graph matrices to derive spectral radius inequalities.

Unified approach to spectral radius bounds for various graph-related matrices.

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.