On the spectra of strong power graphs of finite groups

TL;DR

This paper derives the characteristic polynomial and computes the spectra of the distance and adjacency matrices of the strong power graph associated with finite groups, providing spectral insights into these algebraic structures.

Contribution

It introduces explicit formulas for the spectra of strong power graphs of finite groups, advancing understanding of their algebraic and spectral properties.

Findings

Derived the characteristic polynomial of the strong power graph.

Computed the adjacency spectrum of the strong power graph.

Computed the distance spectrum of the strong power graph.

Abstract

We give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum.