Discussiones Mathematicae Graph Theory 30(2) (2010) 185-199
doi: 10.7151/dmgt.1486

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ON THE (2,2)-DOMINATION NUMBER OF TREES

You Lu,  Xinmin Hou  and  Jun-Ming Xu

Department of Mathematics
University of Science and Technology of China
Hefei, Anhui, 230026, China
e-mail: xmhou@ustc.edu.cn

Abstract

Let γ(G) and γ2,2(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] ≤ γ2,2(T) ≤ 2γ(T). Moreover, we characterize all the trees achieving the equalities.

Keywords: domination number, total domination number, (2,2)-domination number.

2010 Mathematics Subject Classification: 05C69.

References

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Received 19 September 2008
Revised 4 June 2009
Accepted 4 June 2009