Γ-supermagic labeling of products of two cycles with dihedral groups

A Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that for every vertex x∈V a product of labels of all edges incident with x is equal to the same element µ∈Γ. A Γ-supermagic labeling of the Cartesian product of two cycles, CmℹCn for every m,n≥3 of the same parity was found recently [5, 6] for all Abelian groups of order 2mn. In this paper we present a Dk-supermagic labeling of the Cartesian, direct, and strong product by dihedral group Dk for any m,n≥3.