Some properties of Graph Laplacians of cyclic groups

TL;DR

This paper explores the spectral properties of Laplacian matrices of cyclic groups, analyzing their characteristic polynomials to understand their eigenvalues and relationships between different groups.

Contribution

It provides new theoretical insights into the spectra of Laplacian matrices of cyclic groups and establishes relationships between their eigenvalues.

Findings

Derived properties of the spectra of cyclic groups' Laplacian matrices

Established relationships between spectra of different cyclic groups

Proved several assertions about characteristic polynomials

Abstract

In this paper we investigate a spectra of the Laplacian matrix of cyclic groups using the properties of their characteristic polynomials. We have proved several assertions about the relationship between the spectra of different groups.