Upper bounds for α-domination parameters

Andrei Gagarin, Anush Poghosyan, Vadim Zverovich

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We provide a new upper bound for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees. This result generalises the well-known Caro-Roditty bound for the domination number of a graph. The same probabilistic construction is used to generalise another well-known upper bound for the classical domination in graphs. Using a different probabilistic construction, we prove similar upper bounds for the α-rate domination number, which combines the concepts of α-domination and k-tuple domination.

Original languageEnglish
Pages (from-to)513-520
Number of pages8
JournalGraphs and Combinatorics
Volume25
Issue number4
DOIs
Publication statusPublished - 12 Dec 2009

Keywords

  • α-Domination
  • α-Rate domination
  • Domination
  • Graph
  • Probabilistic method

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

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