On Sum of Powers of the Laplacian Eigenvalues of Power Graphs of Certain Finite Groups

The power graph G(G) 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. Here we concentrate on sum of powers of the non-zero Laplacian eigenvalues of G(Zn) and G(Dn). As a result we obtain bounds for Laplacian-energy-like (LEL) invariant of the same graphs.