Restrained domination in unicyclic graphs
Johannes H. Hattingh ; Ernst J. Joubert ; Marc Loizeaux ; Andrew R. Plummer ; Lucas van der Merwe
Discussiones Mathematicae Graph Theory, Tome 29 (2009), p. 71-86 / Harvested from The Polish Digital Mathematics Library
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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 γr(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 γr(U)≥⎡n/3⎤, and provide a characterization of graphs achieving this bound.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:270570 
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Johannes H. Hattingh; Ernst J. Joubert; Marc Loizeaux; Andrew R. Plummer; Lucas van der Merwe. Restrained domination in unicyclic graphs. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 71-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1433/

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