Group Distance Magic Labeling of Graphs and their Direct Product

Abstract

A graph G is said to have the group distance magic labeling if there exists an abelian group H and one-one map A from the vertex set of G to the group elements such that x∈N (u) A(x) = μ for all u ∈ V, where N (u) is the open neighborhood of u and μ ∈ H is the magic constant, more specifically such graph is called H-distance magic graph. In this paper, we prove anti-prism graphs are Z2n, Z2 × Zn, Z3 × Z6m, Z4 × Z6m, and Z6 × Z6m-distance magic graphs. This paper also concludes the group distance magic labeling of direct product of the anti-prism graphs.