Decompositions of graphs via generalized graceful labelings

In [Pasotti, A., On d-graceful labelings, to appear on Ars Combin] a d-divisible α-labeling is defined as a generalization of the classical one of Rosa (see [Rosa, A., On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967), 349–355]) and, similarly to the classical case, it is proved that there exists a link between d-divisible α-labelings of a graph Γ and cyclic Γ-decompositions. In [Benini, A., and Pasotti, A., Decompositions of complete multipartite graphs via generalized graceful labelings, submitted. (arXiv:1210.4370)] we have dealt with the existence of d-divisible α-labelings of caterpillars and certain classes of cycles and hairy cycles and the resulting possible decompositions.