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A characterization of (γₜ,γ₂)-trees

100%

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

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 3

425-435

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.

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

100%

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

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 2

185-199

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

2 Discussiones Mathematicae Graph Theory

2 Hou X.

2 Lu Y.

2 Xu J.-M.

1 Li N.

2 2010

Wyniki wyszukiwania

A characterization of (γₜ,γ₂)-trees

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