In t his Paper

we Prove that the Power graphs of cycles are hamiltonian decomposible.As a consequence

we show that there at least [] edge-disjoint hamiltionian cycles in tie k - the powergraph of a claw-free connected graph . We also determine the automorphism groups of the Powergraphs of directed and undirected cycles. Simple formulae or recursive relations for the number oftrees of some special graphs are deduced.