Adjacency spectra of some subdivision hypergraphs

TL;DR

This paper introduces a subdivision operation for hypergraphs, computes eigenvalues for regular and certain non-regular hypergraphs, and demonstrates how to construct non-isomorphic cospectral hypergraphs using this operation.

Contribution

It defines a subdivision operation for hypergraphs and analyzes its spectral properties, including eigenvalues and cospectral hypergraph construction.

Findings

Eigenvalues of subdivided regular hypergraphs are explicitly computed.

Subdivision operation can generate non-isomorphic cospectral hypergraphs.

Analysis includes various hypergraph types like hyperflowers and squid-like hypergraphs.

Abstract

Here, we define a subdivision operation for a hypergraph and compute all the eigenvalues of the subdivision of regular and certain non-regular hypergraphs. In non-regular hypergraphs, we investigate the power of regular graphs, various types of hyperflowers, and the squid-like hypergraph. Using our subdivision operation, we also show how to construct non-regular non-isomorphic cospectral hypergraphs.