On the Adjacency and Seidel Spectra of Hypergraphs

TL;DR

This paper explores the spectral properties of hypergraphs, establishing relationships between Seidel and adjacency spectra, and computes eigenvalues for specific hypergraph classes, advancing understanding of hypergraph spectra.

Contribution

It introduces new relationships between Seidel and adjacency spectra of hypergraphs and computes eigenvalues for specific hypergraph structures.

Findings

Eigenvalues of certain k-uniform hypergraphs are explicitly computed.

Spectra of the uniform double hyperstar and sunflower hypergraph are estimated.

Seidel spectrum and main Seidel eigenvalues of hyperstar are determined.

Abstract

A hypergraph generalizes the concept of an ordinary graph. In an ordinary graph, edges connect pairs of vertices, whereas in a hypergraph, hyperedges can connect multiple vertices at a time. In this paper, we obtain a relationship between the characteristic polynomial of Seidel and adjacency matrices of hypergraph and also compute all the eigenvalues of some k-uniform hypergraphs. Moreover, we estimate the adjacency and Seidel spectra of the uniform double hyperstar and sunflower hypergraph. In addition to that, we determine the Seidel spectrum and main Seidel eigenvalues of hyperstar.