Signless and normalized Laplacian spectrums of the power graph and its supergraph of certain finite groups

Let G be a finite group. The power graph P(G) and its supergraph, cyclic graph ΓG are two simple graphs with the same vertex set G. Two elements x,y ∈ G are adjacent in the power graph if and only if one is a power of the other. They are joined in ΓG if and only if ⟨x,y⟩ is cyclic. The aim of this article is to compute the signless and normalized Laplacian spectrums of the power graph, its main supergraph and cyclic graph of dihedral and dicyclic groups.