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In this paper, we use the product ⊗h in order to study super edge-magic labelings, bi-magic labelings and optimal k-equitable labelings. We establish, with the help of the product ⊗h, new relations between super edge-magic labelings and optimal k-equitable labelings and between super edge-magic labelings and edge bi-magic labelings. We also introduce new families of graphs that are inspired by the family of generalized Petersen graphs. The concepts of super bi-magic and r-magic labelings are also introduced and discussed, and open problems are proposed for future research.
CitationLópez, S.C.; Muntaner Batle, F.A.; Rius, M. Bi-magic and other generalizations of super edge-magic labelings. "Bulletin of the Australian Mathematical Society", 15 Juny 2011, vol. 84, núm. 1, p. 137-152.
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