Orientable Z n -distance magic graphs

Sylwia Cichacz, Bryan Freyberg, Dalibor Froncek

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let G = (V, E) be a graph of order n. A distance magic labeling of G is a bijection ℓ: V → {1, 2, . . ., n} for which there exists a positive integer k such that P x ∈N(v) ℓ(x) = k for all v ∈ V, where N(v) is the open neighborhood of v. Tuttes flow conjectures are a major source of inspiration in graph theory. In this paper we ask when we can assign n distinct labels from the set {1, 2, . . ., n} to the vertices of a graph G of order n such that the sum of the labels on heads minus the sum of the labels on tails is constant modulo n for each vertex of G. Therefore we generalize the notion of distance magic labeling for oriented graphs.

Original languageEnglish (US)
Pages (from-to)533-546
Number of pages14
JournalDiscussiones Mathematicae - Graph Theory
Volume39
Issue number1
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
1This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of Ministry of Science and Higher Education.

Keywords

  • Digraph
  • Distance magic graph
  • Flow graph

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