Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 5, No 2 (2017): Electronic Journal of Graph Theory and Applications

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

Bryan Freyberg (Department of Mathematics and Computer Science, Southwest Minnesota State University, Marshall, MN 56258)
Melissa Keranen (Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931)



Article Info

Publish Date
16 Oct 2017

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.

Copyrights © 2017






Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...