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Restrained domination in unicyclic graphs

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Hattingh J., Joubert E., Loizeaux M., Plummer A., van der Merwe L.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 1

71-86

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Hattingh J.

1 Joubert E.

1 Loizeaux M.

1 Plummer A.

1 van der Merwe L.

1 2009

Wyniki wyszukiwania

Restrained domination in unicyclic graphs