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 and one-one map ℓ from the vertex set of G to the group elements, such that y NG+xy-y NG-xy=μ for all x V, where NGx is the open neighborhood of x, and μ is the magic constant; more specifically, such graph is called orientable -distance magic graph. In this study, we prove directed antiprism graphs are orientable 2n, 2×n, and 3×6m-distance magic graphs. This study also concludes the orientable group distance magic labeling of direct product of the said directed graphs.