The Laplacian spectral moments of power hypergraphs

TL;DR

This paper derives formulas for the Laplacian spectral moments of power hypergraphs and demonstrates that certain graphs can be uniquely identified by their high-order Laplacian spectra using these moments.

Contribution

It introduces new expressions for spectral moments of power hypergraphs and shows their potential in graph identification based on spectral data.

Findings

Formulas for spectral moments expressed via graph parameters

Some graphs are uniquely determined by their high-order Laplacian spectrum

Advances spectral graph theory with hypergraph spectral analysis

Abstract

The $d$-th order Laplacian spectral moment of a $k$-uniform hypergraph is the sum of the $d$-th powers of all eigenvalues of its Laplacian tensor. In this paper, we obtain some expressions of the Laplacian spectral moments for $k$-uniform power hypergraphs, and these expressions can be represented by some parameters of graphs. And we show that some graphs can be determined by their high-order Laplacian spectrum by using the Laplacian spectral moments of power hypergraphs.