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[Gallian] surveys graceful graphs, i.e. graphs with a graceful labelling, and lists the graphs whose status is known.

In regards to Constraint Programming Petrie and Smith [PetrieSmith] in 2003 have shown that K4×P2, K4×P3, K4×P4, K4×P5, are graceful. They also proved that K3×P3 and K6×P2 are not graceful. In 2010 Smith and Puget [SmithPuget] extended this work to show that K7×P2, K8×P2, K9×P2 and K10×P2 are not graceful.