Distance magic labelings of hypercubes

A distance magic labeling of a graph G is a bijective assignment of labels from {1, 2, …, |V (G)|} to the vertices of G such that the sum of labels on neighbors of u is the same for all vertices u. We show that the n-dimensional hypercube has a distance magic labeling for every n ≡ 2 ( mod 4 ) . It is known that this condition is also necessary. This completes solution of a conjecture posed by Acharya et al. [B. D. Acharya, S. B. Rao, T. Singh and V. Parameswaran, Neighborhood magic graphs, In National Conference on Graph Theory, Combinatorics and Algorithm, 2004].