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

Bryan Freyberg, Melissa Keranen

Research output: Contribution to journalArticlepeer-review

Abstract

The following generalization of distance magic graphs was introduced in [2]. A directed ℤn- distance magic labeling of an oriented graph G = (V,A) of order n is a bijection ℓ: V → ℤn with the property that there is a μ ∈ ℤn (called the magic constant) such that If for a graph G there exists an orientation G such that there is a directed ℤn-distance magic labeling ℓ for G, we say that G is orientable ℤn-distance magic and the directed ℤn-distance magic labeling ℓ we call an orientable ℤn-distance magic labeling. In this paper, we find orientable ℤn- distance magic labelings of the Cartesian product of cycles. In addition, we show that even-ordered hypercubes are orientable ℤn-distance magic.

Original languageEnglish (US)
Pages (from-to)304-311
Number of pages8
JournalElectronic Journal of Graph Theory and Applications
Volume5
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Directed distance magic labeling
  • Distance magic graph
  • Orientable ℤ-distance magic labeling

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