Lexicographical ordering by spectral moments of bicyclic hypergraphs

TL;DR

This paper investigates the spectral moment ordering of bicyclic hypergraphs, identifying the extremal hypergraphs in this order for linear bicyclic uniform hypergraphs with specified girth and edge count.

Contribution

It provides the first and last hypergraphs in the spectral moment order for linear bicyclic uniform hypergraphs with given girth and edges, advancing understanding of spectral properties in hypergraph theory.

Findings

Identified the extremal hypergraphs in the spectral moment order.

Established the ordering for linear bicyclic uniform hypergraphs with given parameters.

Contributed to spectral hypergraph theory by characterizing extremal structures.

Abstract

For bicyclic hypergraphs, ordering by spectral moment ($S$-order) is investigated in this paper. We give the first and last hypergraphs in an $S$-order of linear bicyclic uniform hypergraphs with given girth and number of edges.