Total restrained domination in unicyclic graphs

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

Total restrained domination in unicyclic graphs

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

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 γ_tr(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 γ_tr(U) ≥ [n/2], and provide a characterization of graphs achieving this bound.

Original language	English
Pages (from-to)	81-95
Number of pages	15
Journal	Utilitas Mathematica
Volume	82
Publication status	Published - Jul 2010

Keywords

Total restrained domination
Unicyclic graph

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Cite this

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AU - Hattingh, Johannes H.

AU - Joubert, Ernst J.

AU - Jonck, Elizabeth

AU - Plummer, Andrew R.

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N2 - 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.

AB - 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.

KW - Total restrained domination

KW - Unicyclic graph

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JO - Utilitas Mathematica

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ER -

Total restrained domination in unicyclic graphs

Abstract

Keywords

ASJC Scopus subject areas

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