Γ-Supermagic Labeling of 4-Regular Archimedean Graphs 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. D2k-supermagic labelings of the Cartesian, direct, and strong product of cycles Cm and Cn by dihedral group D2k for any m, n ≥ 3 were found recently. In this paper we present D2k -supermagic labelings of the four 4-regular Archimedean graphs, antiprisms, and their non-planar generalizations, j-antiprisms.