Spectra of Power Graphs of Finite Groups

In this book, the spectra of power graphs associated with finite groups have been explored. The power graph of a finite group G is an undirected graph whose vertex set is G and any two vertices in the graph are adjacent if and only if one of them is an integral power of the power. We first study the signless Laplacian spectra of the power graph of the finite cyclic group Z n and the dihedral group D n. When the number of vertices is large enough, we provide lower and upper bounds on the largest signless Laplacian eigenvalue of power graph of finite cyclic and dihedral groups. We also study the distance signless Laplacian spectra of power graphs of finite cyclic and dihedral groups.