# Restrained domination in unicyclic graphs

Johannes H. Hattingh; Ernst J. Joubert; Marc Loizeaux; Andrew R. Plummer; Lucas van der Merwe

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 1, page 71-86
- ISSN: 2083-5892

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top## Abstract

top## How to cite

topJohannes H. Hattingh, et al. "Restrained domination in unicyclic graphs." Discussiones Mathematicae Graph Theory 29.1 (2009): 71-86. <http://eudml.org/doc/270570>.

@article{JohannesH2009,

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 by $γ_r(G)$, 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 $γ_r(U) ≥ ⎡n/3⎤$, and provide a characterization of graphs achieving this bound.},

author = {Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas van der Merwe},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {restrained domination; unicyclic graph},

language = {eng},

number = {1},

pages = {71-86},

title = {Restrained domination in unicyclic graphs},

url = {http://eudml.org/doc/270570},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Johannes H. Hattingh

AU - Ernst J. Joubert

AU - Marc Loizeaux

AU - Andrew R. Plummer

AU - Lucas van der Merwe

TI - Restrained domination in unicyclic graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 1

SP - 71

EP - 86

AB - 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 $γ_r(G)$, 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 $γ_r(U) ≥ ⎡n/3⎤$, and provide a characterization of graphs achieving this bound.

LA - eng

KW - restrained domination; unicyclic graph

UR - http://eudml.org/doc/270570

ER -

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