Restrained domination in claw-free graphs with minimum degree at least two

Johannes H. Hattingh, Ernst J. Joubert

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Let G = (V, E) be a graph. A set S ⊇ V is a restrained dominating set if every vertex in V - S is adjacent to a vertex in S and to a vertex in V - S. The restrained domination number of G, denoted γr(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is claw-free with minimum degree at least two and G ∉ {C4, C5,C7,C8,C11,C14,C17}, then γr(G) ≤.

Original languageEnglish
Pages (from-to)693-706
Number of pages14
JournalGraphs and Combinatorics
Volume25
Issue number5
DOIs
Publication statusPublished - Feb 2010

Keywords

  • Claw-free graph
  • Domination
  • Graph
  • Order of a graph
  • Restrained domination
  • Upper bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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