Distance magic cartesian products of graphs

Sylwia Cichacz; Dalibor Froncek; Elliot Ivrop; Christopher Raridand

doi:10.7151/dmgt.1852

Distance magic cartesian products of graphs

Sylwia Cichacz, Dalibor Froncek, Elliot Ivrop, Christopher Raridand

Mathematics & Statistics

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15 Scopus citations

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.

Original language	English (US)
Pages (from-to)	299-308
Number of pages	10
Journal	Discussiones Mathematicae - Graph Theory
Volume	36
Issue number	2
DOIs	https://doi.org/10.7151/dmgt.1852
State	Published - 2016

Bibliographical note

Funding Information:
Supported by National Science Centre Grant No. 2011/01/D/ST1/04104.

Keywords

Cartesian product
Complete multipartite graph
Cycle
Distance magic labeling
Hypercube
Magic constant
Sigma labeling

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Distance magic cartesian products of graphs

Abstract

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Keywords

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