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Bryan Freyberg
Department of Mathematics and Computer Science, Southwest Minnesota State University, Marshall, MN 56258
Electrical & Electronics Engineering

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Orientable Z_n-distance magic labeling of the Cartesian product of many cycles Bryan Freyberg; Melissa Keranen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (2017): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2017.5.2.11

Abstract

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.
Co-Authors Melissa Keranen