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On the Totalk-Domination in Graphs

100%

Bermudo S., Hernández-Gómez J. C., Sigarreta J. M.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

301-317

Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.

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Some results on total domination in direct products of graphs

88%

Dorbec P., Gravier S., Klavžar S., Spacapan S.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

103-112

Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Bermudo S.

1 Dorbec P.

1 Gravier S.

1 Hernández-Gómez J. C.

1 Klavžar S.

1 Sigarreta J. M.

1 Spacapan S.

1 2018

1 2006

Wyniki wyszukiwania

On the Totalk-Domination in Graphs

Some results on total domination in direct products of graphs