Journal of Prime Research in Mathematics

Group Distance Magic Labeling of Product of Graphs

Wasim Ashraf\(^{a,*}\), Hani Shaker\(^a\)

\(^a\)Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan.


Correspondence should be addressed to:,


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 uV, 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×ℤst, ℤ3 × ℤ2t and ℤ3 × ℤst distance magic graphs.


Group Distance Magic Labeling, Anti-prism, Cycles, Direct Product.