Total restrained domination in unicyclic graphs

Johannes H. Hattingh, Ernst J. Joubert, Elizabeth Jonck, Andrew R. Plummer

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Let G = (V, E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex in V is adjacent to a vertex in S and every vertex of V - S is adjacent to a vertex in V - S. The total restrained domination number of G, denoted by γtr(G), is the minimum cardinality of a total 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 γtr(U) ≥ [n/2], and provide a characterization of graphs achieving this bound.

Original languageEnglish
Pages (from-to)81-95
Number of pages15
JournalUtilitas Mathematica
Publication statusPublished - Jul 2010


  • Total restrained domination
  • Unicyclic graph

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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