Orientable Z_n-distance magic labeling of the Cartesian product of many cycles - Bryan Freyberg; Melissa Keranen (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2017)
The following generalization of distance magic graphs was introduced in [2]. A directed Z_n-distance magic labeling of an oriented graph G=(V,A) of order n is a bijection V → Z_n with the property that there is a μ Z_n (called the magic constant) such that w(x)= _yN_G^+(x) (y) - _yN_G^-(x) (y)= μ for every x V(G). If for a graph G there exists an orientation G such that there is a directed Z_n-distance magic labeling for G, we say that G is orientable Z_n-distance magic and the directed Z_n-distance magic labeling we call an orientable Z_n-distance magic labeling. In this paper, we find orientable Z_n-distance magic labelings of the Cartesian product of cycles. In addition, we show that even-ordered hypercubes are orientable Z_n-distance magic.