Distance magic graphs G x Cn

A Gamma-distance magic labeling of a graph G = (V, E) with vertical bar V vertical bar = n is a bijection f from V to an Abelian group Gamma of order n such that the weight w(x) = Sigma(y is an element of NG(x)) f(y) of every vertex x is an element of V is equal to the same element mu is an element of Gamma, called the magic constant. In this paper we will show that if G is a graph of order n = 2(p)(2k + 1) for some natural numbers p, k such that deg(v) equivalent to c (mod 2(p+2)) for some constant c for any v is an element of V(G), then there exists a Gamma-distance magic labeling for any Abelian group Gamma of order 4n for the direct product G X C-4. Moreover if c is even, then there exists a Gamma-distance magic labeling for any Abelian group P of order 8n for the direct product G X C-8. (C) 2014 Elsevier B.V. All rights reserved.