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 $\overrightarrow{G}=(V,A)$ of order n is a bijection $\overrightarrow{\ell}\colon V \rightarrow Z_n$ with the property that there is a $\mu \in Z_n$ (called the magic constant) such that w(x)= \sum_{y\in N_{G}^{+}(x)} \overrightarrow{\ell}(y) - \sum_{y\in N_{G}^{-}(x)} \overrightarrow{\ell}(y)= \mu$for every x \in V(G). If for a graph G there exists an orientation$\overrightarrow{G}$such that there is a directed Z_n-distance magic labeling$\overrightarrow{\ell}$for$\overrightarrow{G}$, we say that G is orientable Z_n-distance magic and the directed Z_n-distance magic labeling$\overrightarrow{\ell}$ 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