TY - JOUR

T1 - Orientable ℤn-distance magic labeling of the Cartesian product of many cycles

AU - Freyberg, Bryan

AU - Keranen, Melissa

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Directed distance magic labeling

KW - Distance magic graph

KW - Orientable ℤ-distance magic labeling

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U2 - 10.5614/ejgta.2017.5.2.11

DO - 10.5614/ejgta.2017.5.2.11

M3 - Article

AN - SCOPUS:85031909641

VL - 5

SP - 304

EP - 311

JO - Electronic Journal of Graph Theory and Applications

JF - Electronic Journal of Graph Theory and Applications

SN - 2338-2287

IS - 2

ER -