Laplacian spectra of power graphs of certain prime-power Abelian groups

Abstract

The power graph [Formula: see text] of a semigroup [Formula: see text] is a simple undirected graph whose vertex set is [Formula: see text] itself, and any two distinct vertices are adjacent if one of them is a power of the other. In this paper, we describe the power graph [Formula: see text] in terms of joins and disjoint unions of complete graphs, and use this to calculate the Laplacian polynomial of [Formula: see text]. We finally calculate the Laplacian polynomial of the power graph [Formula: see text].