The characteristic polynomials of uniform hypercycles with length four

TL;DR

This paper derives trace formulas and characteristic polynomials for 4-length uniform hypercycles, extending spectral graph theory to hypergraphs and providing explicit algebraic expressions for their spectra.

Contribution

It introduces explicit characteristic polynomials for 4-length uniform hypercycles, advancing the spectral analysis of hypergraphs.

Findings

Derived trace formulas for hypercycles of length four

Obtained explicit characteristic polynomials for these hypercycles

Enhanced understanding of spectral properties of uniform hypergraphs

Abstract

Let $C_{m}$ be a cycle with length $m.$ The $k$-uniform hypercycle with length $m$ obtained by adding $k-2$ new vertices in every edge of $C_{m},$ denoted by $C_{m,k}.$ In this paper, we obtain some trace formulas of uniform hypercycles with length four. Moreover, we give the characteristic polynomials of uniform hypercycles with length four.