On regular handicap graphs of even order

Dalibor Fronček, Petr Kovář, Tereza Kovářová, Bohumil Krajc, Michal Kravčenko, Aaron Shepanik, Adam Silber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let G=(V,E) be a simple graph of order n. A bijection f : V→{1,2,…,n} is a handicap labeling of G if there exists an integer ℓ such that ∑u∈N(v)f(u)=ℓ+f(v) for all v∈V, where N(v) is the set of all vertices adjacent to v. Any graph which admits a handicap labeling is a handicap graph. We present an overview of results, which completely answer the question of existence of regular handicap graphs of even order.

Original languageEnglish (US)
Pages (from-to)69-76
Number of pages8
JournalElectronic Notes in Discrete Mathematics
Volume60
DOIs
StatePublished - Jul 2017

Keywords

  • Graph labeling
  • handicap labeling
  • regular graphs

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