Geodesic
On the (2,2)-domination number of trees
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 185-199.

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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.
Keywords: domination number, total domination number, (2,2)-domination number 
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Lu, You; Hou, Xinmin; Xu, Jun-Ming. On the (2,2)-domination number of trees. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 2, pp. 185-199. http://geodesic.mathdoc.fr/item/DMGT_2010_30_2_a0/

[1] T.J. Bean, M.A. Henning and H.C. Swart, On the integrity of distance domination in graphs, Australas. J. Combin. 10 (1994) 29-43.

[2] G. Chartrant and L. Lesniak, Graphs Digraphs (third ed., Chapman Hall, London, 1996).

[3] M. Fischermann and L. Volkmann, A remark on a conjecture for the (k,p)-domination number, Utilitas Math. 67 (2005) 223-227.

[4] M.A. Henning, Trees with large total domination number, Utilitas Math. 60 (2001) 99-106.

[5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (New York, Marcel Deliker, 1998).

[6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (New York, Marcel Deliker, 1998).

[7] T. Korneffel, D. Meierling and L. Volkmann, A remark on the (2,2)-domination number Discuss. Math. Graph Theory 28 (2008) 361-366, doi: 10.7151/dmgt.1411.