The algebraic multiplicity of the spectral radius of a hypertree

TL;DR

This paper investigates the algebraic multiplicity of the spectral radius in uniform hypertrees, providing a novel approach using Poisson Formula and matching polynomials to determine this multiplicity.

Contribution

It introduces a new method combining Poisson Formula and matching polynomials to analyze the algebraic multiplicity of the spectral radius in hypertrees.

Findings

Determined the algebraic multiplicity for the spectral radius of uniform hypertrees.

Established a connection between spectral properties and matching polynomials.

Provided a framework for analyzing spectral multiplicities in hypergraph structures.

Abstract

It is well-known that the spectral radius of a connected uniform hypergraph is an eigenvalue of the hypergraph. However, its algebraic multiplicity remains unknown. In this paper, we use the Poisson Formula and matching polynomials to determine the algebraic multiplicity of the spectral radius of a uniform hypertree.