Group Distance Magic Labeling of Product of Graphs

A graph is a tool used to build the interconnection network that a system requires. Such networks inter-operability is ensured by specific labeling. There are several labelings in the literature, however the Group Distance Magic Labeling is better for graphs. A graph G is described as ℋ-distance magic graph if for an abelian group ℋ, there exist one-one mapping 𝓁 between group elements and vertex set of graph G such that ⅀ _{𝓍 ∈ N(u)} 𝓁(x) = µ for all u ∈ V, where µ is the magic constant belongs to abelian group ℋ and N(u) is u′s free neighborhood. In this article, we prove direct product of anti-prism graphs with nth order cycles are ℤ _2st, ℤ₂×ℤ_st, ℤ₃ × ℤ_2t and ℤ₃ × ℤ_{⅔st distance magic graphs.}