Power graphs via their characteristic polynomial

A power graph is defined a graph that it's vertices are the elements of group and two vertices are adjacent if and only if one of them is a power of the other. Suppose A(X) is the adjacency matrix of graph X. Then the polynomial \chi(X,\lambda)=det(xI-A(X)) is called as characteristic polynomial of X. In this paper,  we compute the characteristic polynomial of all power graphs of order p^۲q, where p,q are distinct prime numbers.