Distance magic cartesian products of graphs

Sylwia Cichacz, Dalibor Froncek, Elliot Ivrop, Christopher Raridand

Research output: Contribution to journalArticlepeer-review

6 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 languageEnglish (US)
Pages (from-to)299-308
Number of pages10
JournalDiscussiones Mathematicae - Graph Theory
Volume36
Issue number2
DOIs
StatePublished - 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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