On Laplacian spectrum of power graphs of finite cyclic and dihedral groups

Abstract

The power graph of a finite group G is the graph whose vertices are the elements of G and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper, we study Laplacian spectrum of the power graph of additive cyclic group and the dihedral group . We show that the Laplacian spectrum of is the union of that of and . We find algebraic connectivity of and give bounds of the same for .