Bounds for the spectral radius of nonnegative matrices

TL;DR

This paper establishes bounds for the spectral radius of nonnegative matrices using average 2-row sums, with characterizations for irreducible cases, and applies these bounds to matrices associated with graphs.

Contribution

It introduces new bounds for the spectral radius of nonnegative matrices and characterizes equality cases for irreducible matrices, extending to graph-related matrices.

Findings

Bounds for spectral radius using average 2-row sums

Characterization of equality cases for irreducible matrices

Applications to various graph-associated matrices

Abstract

We give upper and lower bounds for the spectral radius of a nonnegative matrix by using its average 2-row sums, and characterize the equality cases if the matrix is irreducible. We also apply these bounds to various nonnegative 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.