Adjacency Energy of Hypergraphs

TL;DR

This paper introduces the concept of adjacency energy for hypergraphs, explores its properties, bounds, and how it changes with modifications, and solves extremal problems for specific hypergraph classes.

Contribution

It defines hypergraph energy, derives bounds based on structural and spectral parameters, and analyzes energy variations under modifications, including extremal hyperstar cases.

Findings

Hypergraph energy is never an odd number.

Bounds for hypergraph energy depend on Zagreb index and spectral radius.

Energy varies predictably with vertex/edge removal and division.

Abstract

In this paper, we define and obtain several properties of the (adjacency) energy of a hypergraph. In particular, bounds for this energy are obtained as functions of structural and spectral parameters, such as Zagreb index and spectral radius. We also study how the energy of a hypergraph varies when a vertex/edge is removed or when an edge is divied. In addition, we solved the extremal problem energy for the class of hyperstars, and show that the energy of a hypergraph is never an odd number.