Some bounds on the eigenvalues of uniform hypergraphs

TL;DR

This paper establishes bounds on the spectral radius of adjacency and signless Laplacian tensors of uniform hypergraphs based on vertex degrees, contributing to spectral hypergraph theory.

Contribution

It provides new bounds for the spectral radius of adjacency and signless Laplacian tensors in uniform hypergraphs, linking spectral properties to vertex degrees.

Findings

Derived bounds for spectral radius of adjacency tensor

Derived bounds for spectral radius of signless Laplacian tensor

Linked spectral bounds to vertex degree distributions

Abstract

Let $\mathcal{H}$ be a uniform hypergraph. Let $\mathcal{A(H)}$ and $\mathcal{Q(H)}$ be the adjacency tensor and the signless Laplacian tensor of $\mathcal{H}$, respectively. In this note we prove several bounds for the spectral radius of $\mathcal{A(H)}$ and $\mathcal{Q(H)}$ in terms of the degrees of vertices of $\mathcal{H}.$