Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs

TL;DR

This paper establishes precise upper bounds for the spectral radii of uniform hypergraphs using vertex degrees and compares these bounds with existing results.

Contribution

It introduces sharp bounds for both ordinary and signless Laplacian spectral radii based on average degrees, enhancing understanding of hypergraph spectral properties.

Findings

Derived sharp upper bounds for spectral radii.

Provided a lower bound for the ordinary spectral radius.

Compared new bounds with existing bounds to demonstrate improvements.

Abstract

We give sharp upper bounds for the ordinary spectral radius and signless Laplacian spectral radius of a uniform hypergraph in terms of the average $2$-degrees or degrees of vertices, respectively, and we also give a lower bound for the ordinary spectral radius. We also compare these bounds with known ones.