Decompositions into generalized Petersen graphs via graceful labelings

We prove that the generalized Petersen graph P 8 n , 3 admits an α-labeling for any integer n ⩾ 1 confirming that the conjecture posed by A. Vietri in [Vietri, A., Graceful labellings for an infinite class of generalised Petersen graphs, Ars Combin. 81 (2006), 247–255.] is true. We present also a result about the existence of d-divisible α-labelings of P 8 n , 3 . In such a way we obtain cyclic decompositions of the complete graph and of the complete multipartite graph into copies of P 8 n , 3 .