Energies of Hypergraphs

TL;DR

This paper investigates various spectral energies of hypergraphs, providing bounds and relationships between different energy measures, and computes specific energies for power hypergraphs, advancing spectral hypergraph theory.

Contribution

It introduces new bounds and relations for hypergraph energies, including incidence and signless Laplacian energies, and computes these energies for power hypergraphs.

Findings

Bounds for incidence energy in terms of maximum degree, Zagreb index, spectral radius

Relations between hypergraph energies and energies of associated subdivision and line multigraphs

Explicit computation of signless Laplacian energy for power hypergraphs

Abstract

In this paper, we study energies associated with hypergraphs. More precisely, we obtain results for the incidence and the singless Laplacian energies of uniform hypergraphs. In particular, we obtain bounds for the incidence energy as functions of well known parameters, such as maximum degree, Zagreb index and spectral radius. We also relate the incidence and signless Laplacian energies of a hypergraph with the adjacency energies of its subdivision graph and line multigraph, respectively. In addition, we compute the signless Laplacian energy for the class of the power hypergraphs.