On the Laplacian of strong power graphs of finite groups

A. K. Bhuniya, S. Bera

Published 2015-04-23Version 1

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 give a complete characterization of Laplacian spectrum, and find the permanent of the Laplacian matrix of the strong power graph $\mathcal{P}_s(G)$ for any finite group $G$.