Orientable Group Distance Magic Labeling of Directed Graphs

Abstract

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 ∈ N G + x ℓ ⟶ y − ∑ y ∈ N G − x ℓ ⟶ y = μ for all x ∈ V , where N G x 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 ℤ 2 n , ℤ 2 × ℤ n , and ℤ 3 × ℤ 6 m -distance magic graphs. This study also concludes the orientable group distance magic labeling of direct product of the said directed graphs.