Given a group G, we de ne the power graph P(G) as follows: the vertices are the elements of G and two vertices x and y are joined by an edge if hxi hyi or hyi hxi. Obviously the power graph of any group is always connected, because the identity element of the group is adjacent to all other vertices. We consider (G), the number of spanning trees of the power graph associated with nite group G. The purpose of this paper is to nd some results concerning the complexity (G) for a nite group G.
