Displaying similar documents to “Remarks on restrained domination and total restrained domination in graphs”

Induced-paired domatic numbers of graphs

Bohdan Zelinka (2002)

Mathematica Bohemica

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A subset D of the vertex set V ( G ) of a graph G is called dominating in G , if each vertex of G either is in D , or is adjacent to a vertex of D . If moreover the subgraph < D > of G induced by D is regular of degree 1, then D is called an induced-paired dominating set in G . A partition of V ( G ) , each of whose classes is an induced-paired dominating set in G , is called an induced-paired domatic partition of G . The maximum number of classes of an induced-paired domatic partition of G is the induced-paired...

Domination in bipartite graphs and in their complements

Bohdan Zelinka (2003)

Czechoslovak Mathematical Journal

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The domatic numbers of a graph G and of its complement G ¯ were studied by J. E. Dunbar, T. W. Haynes and M. A. Henning. They suggested four open problems. We will solve the following ones: Characterize bipartite graphs G having d ( G ) = d ( G ¯ ) . Further, we will present a partial solution to the problem: Is it true that if G is a graph satisfying d ( G ) = d ( G ¯ ) , then γ ( G ) = γ ( G ¯ ) ? Finally, we prove an existence theorem concerning the total domatic number of a graph and of its complement.

Independent transversal domination in graphs

Ismail Sahul Hamid (2012)

Discussiones Mathematicae Graph Theory

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A set S ⊆ V of vertices in a graph G = (V, E) is called a dominating set if every vertex in V-S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γ i t ( G ) . In this paper we begin an investigation of this parameter.