Restrained domination in unicyclic graphs

Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas Van Der Merwe

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 by yr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then yr(U) ≥ d n 3 e, and provide a characterization of graphs achieving this bound.

Original languageEnglish
Pages (from-to)71-86
Number of pages16
JournalDiscussiones Mathematicae - Graph Theory
Issue number1
Publication statusPublished - 2009


  • Restrained domination
  • Unicyclic graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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