E-cospectral hypergraphs and some hypergraphs determined by their spectra

TL;DR

This paper introduces a method for constructing E-cospectral hypergraphs and identifies certain hypergraphs uniquely determined by their spectra, advancing spectral hypergraph theory.

Contribution

It presents a Godsil-McKay-like switching method for creating E-cospectral hypergraphs and demonstrates some hypergraphs are uniquely identified by their spectra.

Findings

A new construction method for E-cospectral hypergraphs

Identification of hypergraphs determined by their spectra

Extension of spectral techniques to hypergraph analysis

Abstract

Two $k$-uniform hypergraphs are said to be cospectral (E-cospectral), if their adjacency tensors have the same characteristic polynomial (E-characteristic polynomial). A $k$-uniform hypergraph $H$ is said to be determined by its spectrum, if there is no other non-isomorphic $k$-uniform hypergraph cospectral with $H$. In this note, we give a method for constructing E-cospectral hypergraphs, which is similar with Godsil-McKay switching. Some hypergraphs are shown to be determined by their spectra.