Lexicographical ordering of hypergraphs via spectral moment

TL;DR

This paper studies the lexicographical ordering of hypergraphs based on spectral moments, characterizing extremal hypergraphs within specific classes such as hypertrees and unicyclic hypergraphs.

Contribution

It provides characterizations of the first and last hypergraphs in the spectral $S$-order for uniform hypertrees and linear unicyclic hypergraphs with fixed girth.

Findings

Identified the extremal hypergraphs in the $S$-order for uniform hypertrees.

Determined the last hypergraph in the $S$-order for linear unicyclic uniform hypergraphs.

Extended spectral ordering concepts to classes of hypergraphs.

Abstract

The lexicographical ordering of hypergraphs via spectral moments is called the $S$-order of hypergraphs.In this paper, the $S$-order of hypergraphs is investigated.We characterize the first and last hypergraphs in an $S$-order of all uniform hypertrees and all linear unicyclic uniformhypergraphs with given girth, respectively. And we give the last hypergraph in an $S$-order of all linear unicyclic uniform hypergraphs.