On some characterizations of strong power graphs of finite groups

Abstract

Let $G$ be a finite group of order $n$. The strong power graph ${\mathcal{P}}_s(G)$ of $G$ is the undirected graph whose vertices are the elements of $G$ such that two distinct vertices $a$ and $b$ are adjacent if $a^{m_1}$=$b^{m_2}$ for some positive integers $m_1,m_2<n$. In this article we classify all groups $G$ for which ${\mathcal{P}}_s(G)$ is line graph and Caley graph. Spectrum and permanent of the Laplacian matrix of the strong power graph ${\mathcal{P}}_s(G)$ are found for any finite group $G$.

13 pages

Cited by in corpus (1)

• On the spectra of strong power graphs of finite groups