Orientable Group Distance Magic Labeling of Directed Graphs

A directed graph G is said to have the orientable group distance magic labeling if there exists an abelian group ℋ and one-one map ℓ from the vertex set of G to the group elements, such that ∑y∈NG+xℓ⟶y−∑y∈NG−xℓ⟶y=μ for all x∈V, where NGx is the open neighborhood of x, and μ∈ℋ is the magic constant; more specifically, such graph is called orientable ℋ-distance magic graph. In this study, we prove directed antiprism graphs are orientable ℤ2n, ℤ2×ℤn, and ℤ3×ℤ6m-distance magic graphs. This study also concludes the orientable group distance magic labeling of direct product of the said directed graphs.