Sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor and its applications

TL;DR

This paper derives precise bounds for the spectral radius of nonnegative weakly irreducible tensors and applies these results to hypergraph spectral properties, enhancing understanding of tensor and hypergraph spectra.

Contribution

It introduces sharp bounds for the spectral radius of nonnegative weakly irreducible tensors and applies them to hypergraph spectral analysis, providing new theoretical tools.

Findings

Established sharp bounds for tensor spectral radius

Applied bounds to hypergraph adjacency spectral radius

Extended results to signless Laplacian spectral radius

Abstract

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor. We also apply these bounds to the adjacency spectral radius and signless Laplacian spectral radius of a uniform hypergraph.