The characteristic polynomial of sunflowers

TL;DR

This paper derives the eigenvalues and spectral moments of sunflowers, a special class of hypergraphs, providing an explicit formula for their characteristic polynomial.

Contribution

It introduces a method to compute the characteristic polynomial of sunflowers, advancing spectral hypergraph theory.

Findings

Explicit formula for the characteristic polynomial of sunflowers

Eigenvalues and spectral moments are determined

Spectral properties of sunflowers are characterized

Abstract

A uniform hypergraph is called a sunflower if all of its hyperedges intersect in the same set of vertices. In this paper, we determine the eigenvalues and spectral moments of a sunflower, thereby obtaining an explicit formula for its characteristic polynomial.