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Total domination of Cartesian products of graphs

100%

Hou X.

Discussiones Mathematicae Graph Theory

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2007

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tom 27

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nr 1

175-178

EN

Let γₜ(G) and $γ_{pr}(G)$ denote the total domination and the paired domination numbers of graph G, respectively, and let G □ H denote the Cartesian product of graphs G and H. In this paper, we show that γₜ(G)γₜ(H) ≤ 5γₜ(G □ H), which improves the known result γₜ(G)γₜ(H) ≤ 6γₜ(G □ H) given by Henning and Rall.

2

A characterization of (γₜ,γ₂)-trees

51%

Lu Y., Hou X., Xu J.-M., Li N.

Discussiones Mathematicae Graph Theory

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2010

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tom 30

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nr 3

425-435

EN

Let γₜ(G) and γ₂(G) be the total domination number and the 2-domination number of a graph G, respectively. It has been shown that: γₜ(T) ≤ γ₂(T) for any tree T. In this paper, we provide a constructive characterization of those trees with equal total domination number and 2-domination number.

3

On the (2,2)-domination number of trees

51%

Lu Y., Hou X., Xu J.-M.

Discussiones Mathematicae Graph Theory

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2010

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tom 30

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nr 2

185-199

EN

Let γ(G) and $γ_{2,2}(G)$ denote the domination number and (2,2)-domination number of a graph G, respectively. In this paper, for any nontrivial tree T, we show that $(2(γ(T)+1))/3 ≤ γ_{2,2}(T) ≤ 2γ(T)$. Moreover, we characterize all the trees achieving the equalities.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

3 Hou X.

2 Lu Y.

2 Xu J.-M.

1 Li N.

2 2010

1 2007

Total domination of Cartesian products of graphs

A characterization of (γₜ,γ₂)-trees

On the (2,2)-domination number of trees