Orientable ℤ_n-distance magic labeling of the Cartesian product of many cycles

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 ℓ: V → ℤ_n with the property that there is a μ ∈ ℤ_n (called the magic constant) such that If for a graph G there exists an orientation G such that there is a directed ℤ_n-distance magic labeling ℓ for G, we say that G is orientable ℤ_n-distance magic and the directed ℤ_n-distance magic labeling ℓ 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.