On the Estrada Index and Spectral Properties of $k$-Uniform Hypergraphs

TL;DR

This paper investigates spectral properties of $k$-uniform hypergraphs, providing bounds on eigenvalues and Estrada index, and characterizes hypergraphs with specific spectral features, advancing understanding of hypergraph spectra.

Contribution

It introduces new bounds for eigenvalues and Estrada index of $k$-uniform hypergraphs, and characterizes hypergraphs with two distinct eigenvalues.

Findings

Bound for sum of largest eigenvalues established

Characterization of hypergraphs with two distinct eigenvalues

Bounds for Estrada index based on edges, order, and energy

Abstract

Various properties of a hypergraph can be explored through its spectrum. In this paper,we estimate the bound for the sum of $t,\,t\in[1,n]$, largest eigenvalues of a $k$-uniform hypergraph of order $n$. Also, we characterize the $k$-uniform hypergraph with two distinct eigenvalues. We establish bounds for the Estrada index of $k$-uniform hypergraphs based on their number of edges, order and energy. In addition, we obtain the second largest Estrada index among the unicyclic hypergraphs.