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Restrained domination in unicyclic graphs

100%

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.

Domination Parameters of a Graph and its Complement

61%

Desormeaux W. J., Haynes T. W., Henning M. A.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

203-215

A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G. Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Desormeaux W. J.

1 Hattingh J.

1 Haynes T. W.

1 Henning M. A.

1 Joubert E.

1 Loizeaux M.

1 Plummer A.

1 van der Merwe L.

1 2018

1 2009

Wyniki wyszukiwania

Restrained domination in unicyclic graphs

Domination Parameters of a Graph and its Complement