# Distance Magic Cartesian Products of Graphs

Sylwia Cichacz; Dalibor Froncek; Elliot Krop; Christopher Raridan

Discussiones Mathematicae Graph Theory (2016)

- Volume: 36, Issue: 2, page 299-308
- ISSN: 2083-5892

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topSylwia Cichacz, et al. "Distance Magic Cartesian Products of Graphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 299-308. <http://eudml.org/doc/277122>.

@article{SylwiaCichacz2016,

abstract = {A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → \{1, . . . , n\} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant. In this paper, we show that hypercubes with dimension divisible by four are not distance magic. We also provide some positive results by proving necessary and sufficient conditions for the Cartesian product of certain complete multipartite graphs and the cycle on four vertices to be distance magic.},

author = {Sylwia Cichacz, Dalibor Froncek, Elliot Krop, Christopher Raridan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {distance magic labeling; magic constant; sigma labeling; Cartesian product; hypercube; complete multipartite graph; cycle},

language = {eng},

number = {2},

pages = {299-308},

title = {Distance Magic Cartesian Products of Graphs},

url = {http://eudml.org/doc/277122},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Sylwia Cichacz

AU - Dalibor Froncek

AU - Elliot Krop

AU - Christopher Raridan

TI - Distance Magic Cartesian Products of Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2016

VL - 36

IS - 2

SP - 299

EP - 308

AB - A distance magic labeling of a graph G = (V,E) with |V | = n is a bijection ℓ : V → {1, . . . , n} such that the weight of every vertex v, computed as the sum of the labels on the vertices in the open neighborhood of v, is a constant. In this paper, we show that hypercubes with dimension divisible by four are not distance magic. We also provide some positive results by proving necessary and sufficient conditions for the Cartesian product of certain complete multipartite graphs and the cycle on four vertices to be distance magic.

LA - eng

KW - distance magic labeling; magic constant; sigma labeling; Cartesian product; hypercube; complete multipartite graph; cycle

UR - http://eudml.org/doc/277122

ER -

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