In this paper we introduced the definition of perfect foldingof graphs and we proved that cycle graphs of even number ofedges can be perfectly folded while that of odd number ofedges can be perfectly folded to C3 . Also we proved thatwheel graphs of odd number of vertices can be perfectlyfolded to C3. Finally we proved that if G is a graph of n verticessuch that 2 < clique number =chromatic number=k < n ,then the graph can be perfectly folded to a clique of order k.