K₄xC_n graphs

K₄xP_n graphs have been shown to be graceful for 0 < n < 6 (at least). The question naturally arises whether other cross-product graphs involving K₄ are also graceful. We have shown that K₄xC₃ (= K₄xK₃) is graceful, with 22 non-isomorphic graceful labellings. K₄xC₄ is also graceful, though we have not found all graceful labellings in that case.

K₄xC₃ with a graceful labelling

K₄xC₄ with a graceful labelling